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  • A classification of SNC log symplectic structures on blow-up of projective spaces
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Katsuhiko Okumura

    It is commonly recognized that the classfication of Poisson manifold is a major problem. From the viewpoint of algebraic geometry, holomorphic projective Poisson manifold is the most important target. Poisson structures on the higher dimensional projective varieties was first studied by Lima and Pereira (Lond Math Soc 46(6):1203–1217, 2014). They proved that any Poisson structures with the reduced

    更新日期:2020-08-10
  • Level one Weyl modules for toroidal Lie algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Ryosuke Kodera

    We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody–Eswara Rao–Yokonuma via vertex operators for type ADE and by Iohara–Saito–Wakimoto and Eswara Rao for general type. The twist is given by an action of \(\mathrm {SL}_{2}(\mathbb {Z})\) on the toroidal Lie algebra. As a by-product, we obtain a formula for the character of the level

    更新日期:2020-08-10
  • The duality between F-theory and the heterotic string in $$D=8$$ D = 8 with two Wilson lines
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-07
    Adrian Clingher, Thomas Hill, Andreas Malmendier

    We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank 16. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3

    更新日期:2020-08-08
  • Twisted characters and holomorphic symmetries
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-03
    Ingmar Saberi, Brian R. Williams

    We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the twist explicitly as a family over the space of nilpotent supercharges in minimal supersymmetry. The BV formalism allows one to work with or without auxiliary fields

    更新日期:2020-08-04
  • Cyclotomic expansions of HOMFLY-PT colored by rectangular Young diagrams
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-31
    Masaya Kameyama, Satoshi Nawata, Runkai Tao, Hao Derrick Zhang

    We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any knot.

    更新日期:2020-07-31
  • The Coxeter relations and KP map for non-commuting symbols
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-27
    Adam Doliwa, Masatoshi Noumi

    We give an action of the symmetric group on non-commuting indeterminates in terms of series in the corresponding Mal’cev–Newmann division ring. The action is constructed from the non-Abelian Hirota–Miwa (discrete KP) system. The corresponding companion map, which gives generators of the action, is discussed in the generic case, and the corresponding explicit formulas have been found in the periodic

    更新日期:2020-07-28
  • p -adic boundary laws and Markov chains on trees
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-26
    A. Le Ny, L. Liao, U. A. Rozikov

    In this paper, we consider a potential on general infinite trees with q spin values and nearest-neighbor p-adic interactions given by a stochastic matrix. We show the uniqueness of the associated Markov chain (splitting Gibbs measures) under some sufficient conditions on the stochastic matrix. Moreover, we find a family of stochastic matrices for which there are at least two p-adic Markov chains on

    更新日期:2020-07-26
  • The topology of mobility-gapped insulators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-18
    Jacob Shapiro

    Studying deterministic operators, we define a topology on the space of mobility-gapped insulators such that topological invariants are continuous maps into discrete spaces, we prove that this is indeed the case for the integer quantum Hall effect, and lastly we show why our “insulator” condition makes sense from the point of view of the localization theory using the fractional moments method.

    更新日期:2020-07-18
  • General derivative Thomae formula for singular half-periods
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-16
    J. Bernatska

    The paper develops second Thomae theorem in hyperelliptic case. The main formula, called general Thomae formula, provides expressions for values at zero of the lowest non-vanishing derivatives of theta functions with singular characteristics of arbitrary multiplicity in terms of branch points and period matrix. We call these values derivative theta constants. First and second Thomae formulas follow

    更新日期:2020-07-16
  • Degenerate band edges in periodic quantum graphs
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-13
    Gregory Berkolaiko, Minh Kha

    Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet–Bloch transform. It is often assumed that the extrema generating the band edges are non-degenerate. This paper constructs a family of examples of \({\mathbb {Z}}^3\)-periodic quantum graphs where the non-degeneracy assumption fails: the maximum of the first band is achieved

    更新日期:2020-07-14
  • Irreducibility of the Fermi surface for planar periodic graph operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-13
    Wei Li, Stephen P. Shipman

    We prove that the Fermi surface of a connected doubly periodic self-adjoint discrete graph operator is irreducible at all but finitely many energies provided that the graph (1) can be drawn in the plane without crossing edges, (2) has positive coupling coefficients, (3) has two vertices per period. If “positive” is relaxed to “complex,” the only cases of reducible Fermi surface occur for the graph

    更新日期:2020-07-13
  • Semiclassical asymptotic behavior of orthogonal polynomials
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-09
    D. R. Yafaev

    Our goal is to find asymptotic formulas for orthonormal polynomials \(P_{n}(z)\) with the recurrence coefficients slowly stabilizing as \(n\rightarrow \infty \). To that end, we develop scattering theory of Jacobi operators with long-range coefficients and study the corresponding second-order difference equation. We introduce the Jost solutions \(f_{n}(z)\) of this equation by a condition for \(n\rightarrow

    更新日期:2020-07-09
  • Finite-dimensional irreducible modules of the Bannai–Ito algebra at characteristic zero
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-02
    Hau-Wen Huang

    Assume that \({\mathbb {F}}\) is algebraically closed with characteristic 0. A central extension \({\mathfrak {BI}}\) of the Bannai–Ito algebras is a unital associative \({\mathbb {F}}\)-algebra generated by X, Y, Z, and the relations assert that each of $$\begin{aligned} \{X,Y\}-Z, \quad \{Y,Z\}-X, \quad \{Z,X\}-Y \end{aligned}$$ is central in \({\mathfrak {BI}}\). In this paper, we classify the finite-dimensional

    更新日期:2020-07-02
  • Higher depth quantum modular forms and plumbed 3-manifolds
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-07-02
    Kathrin Bringmann, Karl Mahlburg, Antun Milas

    In this paper, we study new invariants \(\widehat{Z}_{{{\varvec{a}}}}(q)\) attached to plumbed 3-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable q-series at radial limits conjecturally compute WRT invariants of the corresponding plumbed 3-manifold. Here, we investigate the series \(\widehat{Z}_{0}(q)\) for unimodular plumbing H-graphs with six vertices. We prove that

    更新日期:2020-07-02
  • Two-dimensional twistor manifolds and Teukolsky operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-30
    Bernardo Araneda

    The Teukolsky equations are currently the leading approach for analysing stability of linear massless fields propagating in rotating black holes. It has recently been shown that the geometry of these equations can be understood in terms of a connection constructed from the conformal and complex structure of Petrov type D spaces. Since the study of linear massless fields by a combination of conformal

    更新日期:2020-07-01
  • New integrable two-centre problem on sphere in Dirac magnetic field
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-30
    A. P. Veselov, Y. Ye

    We present a new family of integrable versions of the Euler two-centre problem on two-dimensional sphere in the presence of the Dirac magnetic monopole of arbitrary charge. The new systems have very special algebraic potential and additional integral quadratic in momenta, both in classical and quantum versions.

    更新日期:2020-06-30
  • Higher spin $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ s l 2 R -matrix from equivariant (co)homology
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-29
    Dmitri Bykov, Paul Zinn-Justin

    We compute the rational \({{\mathfrak {s}}}{{\mathfrak {l}}}_2\)R-matrix acting in the product of two spin-\(\ell \over 2\) (\({\ell \in {\mathbb {N}}}\)) representations, using a method analogous to the one of Maulik and Okounkov, i.e., by studying the equivariant (co)homology of certain algebraic varieties. These varieties, first considered by Nekrasov and Shatashvili, are typically singular. They

    更新日期:2020-06-29
  • Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-29
    Dorota Kȩpa-Maksymowicz, Yuri Kozitsky

    Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin–spin pair interaction potentials are random and unbounded. A high-temperature uniqueness of such fields is proved to hold under the following conditions: (a) the vertex degree is of tempered growth, i.e., controlled in a certain way; (b) the interaction potentials \(W_{xy}\)

    更新日期:2020-06-29
  • Compactness property of Lie polynomials in the creation and annihilation operators of the q -oscillator
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-28
    Rafael Reno S. Cantuba

    Given a real number q such that \(0

    更新日期:2020-06-28
  • Discriminant and Hodge classes on the space of Hitchin covers
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-27
    Mikhail Basok

    We continue the study of the rational Picard group of the moduli space of Hitchin spectral covers started in Korotkin and Zograf (J Math Phys 59(9):091412, 2018). In the first part of the paper we expand the “boundary”, “Maxwell stratum” and “caustic” divisors introduced in Korotkin and Zograf (2018) via the set of standard generators of the rational Picard group. This generalizes the result of Korotkin

    更新日期:2020-06-27
  • Complexes of marked graphs in gauge theory
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-24
    Marko Berghoff, Andre Knispel

    We review the gauge and ghost cyle graph complexes as defined by Kreimer, Sars and van Suijlekom in “Quantization of gauge fields, graph polynomials and graph homology” and compute their cohomology. These complexes are generated by labelings on the edges or cycles of graphs and the differentials act by exchanging these labels. We show that both cases are instances of a more general construction of

    更新日期:2020-06-24
  • Time operators for quantum walks
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-20
    Daiju Funakawa, Yasumichi Matsuzawa, Itaru Sasaki, Akito Suzuki, Noriaki Teranishi

    We study time operators for discrete-time quantum systems. Quantum walks are typical examples. We construct time operators for one-dimensional homogeneous quantum walks and determine their deficiency indices and spectra. Our time operators always have self-adjoint extensions. This is in contrast to the fact that time operators for continuous-time quantum systems generally have no self-adjoint extensions

    更新日期:2020-06-23
  • Amortized channel divergence for asymptotic quantum channel discrimination
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-18
    Mark M. Wilde, Mario Berta, Christoph Hirche, Eneet Kaur

    It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807–3820, 2009. arXiv:0804.0686) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the

    更新日期:2020-06-18
  • Perfect state transfer on weighted graphs of the Johnson scheme
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-17
    Luc Vinet, Hanmeng Zhan

    We characterize quantum perfect state transfer on real-weighted graphs of the Johnson scheme \({\mathcal {J}}(n,k)\), which represent spin networks with non-nearest neighbor couplings. Given \({\mathcal {J}}(n,k)=\{A_{1},A_{2},\ldots ,A_{k}\}\) and \(A(X) = w_0A_0 + \cdots + w_m A_m\), we show that X has perfect state transfer at time \(\tau \) if and only if \(n=2k\), \(m\ge 2^{\lfloor {\log _2(k)}

    更新日期:2020-06-17
  • Strong integrability of the bi-YB–WZ model
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-15
    Ctirad Klimčík

    We identify the r-matrix governing the Poisson brackets of the matrix elements of the Lax operator of the bi-YB–WZ model.

    更新日期:2020-06-15
  • A gravitational collapse singularity theorem consistent with black hole evaporation
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-11
    E. Minguzzi

    The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work, I show that the causality conditions in Penrose’s theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence

    更新日期:2020-06-11
  • Spacelike deformations: higher-helicity fields from scalar fields
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-11
    Vincenzo Morinelli, Karl-Henning Rehren

    In contrast to Hamiltonian perturbation theory which changes the time evolution, “spacelike deformations” proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike deformations of the complex massless Klein–Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation

    更新日期:2020-06-11
  • A formula for the relative entropy in chiral CFT
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-06-09
    Lorenzo Panebianco

    We prove the QNEC on the Virasoro nets for a class of unitary states extending the coherent states, that is states obtained by applying an exponentiated stress energy tensor to the vacuum. We also verify the Bekenstein Bound by computing the relative entropy on a bounded interval.

    更新日期:2020-06-09
  • Characteristic (Fedosov-)class of a twist constructed by Drinfel’d
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-31
    Jonas Schnitzer

    In a seminal paper, Drinfel’d explained how to associate with every classical r-matrix, which are called triangular r-matrices by some authors, for a Lie algebra \( \mathfrak {g}\) a twisting element based on \({\mathcal {U}}(\mathfrak {g})[[\hbar ]]\), or equivalently a left invariant star product quantizing the left-invariant Poisson structure corresponding to r on the 1-connected Lie group G of

    更新日期:2020-05-31
  • Characters of tangent spaces at torus fixed points and 3 d -mirror symmetry
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-29
    Andrey Smirnov, Hunter Dinkins

    Let X be a Nakajima quiver variety and \(X'\) its 3d-mirror. We consider the action of the Picard torus \({\mathsf {K}}=\mathrm {Pic}(X)\otimes {\mathbb {C}}^{\times }\) on \(X'\). Assuming that \((X')^{{\mathsf {K}}}\) is finite, we propose a procedure for obtaining the \({\mathsf {K}}\)-character of the tangent spaces at the fixed points in terms of certain enumerative invariants of X known as vertex

    更新日期:2020-05-29
  • Poisson vertex algebras in supersymmetric field theories
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-25
    Jihwan Oh, Junya Yagi

    A large class of supersymmetric quantum field theories, including all theories with \({\mathcal {N}}= 2\) supersymmetry in three dimensions and theories with \({\mathcal {N}}= 2\) supersymmetry in four dimensions, possess topological–holomorphic sectors. We formulate Poisson vertex algebras in such topological–holomorphic sectors and discuss some examples. For a four-dimensional \({\mathcal {N}}= 2\)

    更新日期:2020-05-25
  • Chern–Simons–Schrödinger theory on a one-dimensional lattice
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-23
    Hyungjin Huh, Swaleh Hussain, Dmitry E. Pelinovsky

    We propose a gauge-invariant system of the Chern–Simons–Schrödinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square summable sequences for the scalar field. We also study the existence region of the stationary bound states, which depends on the lattice spacing and the nonlinearity power

    更新日期:2020-05-23
  • Variational representations related to Tsallis relative entropy
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-05-07
    Guanghua Shi, Frank Hansen

    We develop variational representations for the deformed logarithmic and exponential functions and use them to obtain variational representations related to the quantum Tsallis relative entropy. We extend Golden–Thompson’s trace inequality to deformed exponentials with deformation parameter \( q\in [0,1], \) thus complementing the second author’s previous study of the cases with deformation parameter

    更新日期:2020-05-07
  • Log expansions from combinatorial Dyson–Schwinger equations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-04-07
    Olaf Krüger

    We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling constant \(\alpha \) and a logarithmic energy scale L—a reordering of terms as \(G(\alpha ,L) = 1 \pm \sum _{j \ge 0} \alpha ^j H_j(\alpha L)\) is the corresponding log expansion. In a first part of this

    更新日期:2020-04-07
  • Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-04-02
    Alexander Tsymbaliuk

    We introduce super Yangians of \(\mathfrak {gl}(V),\mathfrak {sl}(V)\) (in the new Drinfeld realization) associated with all Dynkin diagrams. We show that all of them are isomorphic to the super Yangians introduced by Nazarov (Lett Math Phys 21(2), 123–131, 1991), by identifying them with the corresponding RTT super Yangians. However, their “positive halves” are not pairwise isomorphic, and we obtain

    更新日期:2020-04-02
  • Uniqueness of static, isotropic low-pressure solutions of the Einstein–Vlasov system
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-16
    Maximilian Thaller, Tomohiro Harada

    In Beig and Simon (Commun Math Phys 144:373–390, 1992) the authors prove a uniqueness theorem for static solutions of the Einstein–Euler system which applies to fluid models whose equation of state fulfills certain conditions. In this article it is shown that the result of Beig and Simon (1992) can be applied to isotropic Vlasov matter if the gravitational potential well is shallow. To this end we

    更新日期:2020-03-16
  • Quadratic algebras arising from Hopf operads generated by a single element
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-14
    Anton Khoroshkin

    The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in detail Hopf operads generated by a single skew-symmetric element of arbitrary arity. We explain why the dual space to the space of n-ary operations in these operads are quadratic and Koszul

    更新日期:2020-03-14
  • Yangians and Baxter’s relations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-13
    Huafeng Zhang

    We study a category \({\mathcal {O}}\) of representations of the Yangian associated to an arbitrary finite-dimensional complex simple Lie algebra. We obtain asymptotic modules as analytic continuation of a family of finite-dimensional modules, the Kirillov–Reshetikhin modules. In the Grothendieck ring, we establish the three-term Baxter’s TQ relations for the asymptotic modules. We indicate that Hernandez–Jimbo’s

    更新日期:2020-03-13
  • Central limit theorem for Bose gases interacting through singular potentials
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-12
    Simone Rademacher

    We consider a system of N bosons in the limit \(N \rightarrow \infty \), interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central

    更新日期:2020-03-12
  • Multi-oriented props and homotopy algebras with branes
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-12
    Sergei Merkulov

    We introduce a new category of differential graded multi-oriented props whose representations (called homotopy algebras with branes) in a graded vector space require a choice of a collection of k linear subspaces in that space, k being the number of extra orientations (if \(k=0\) this structure recovers an ordinary prop); symplectic vector spaces equipped with k Lagrangian subspaces play a distinguished

    更新日期:2020-03-12
  • Quantum Hellinger distances revisited
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-10
    József Pitrik, Dániel Virosztek

    This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form \(\phi (A,B)=\mathrm {Tr} \left( (1-c)A + c B - A \sigma B \right) ,\) where \(\sigma \) is an arbitrary Kubo–Ando mean, and \(c \in (0

    更新日期:2020-03-10
  • Hörmander’s method for the characteristic Cauchy problem and conformal scattering for a nonlinear wave equation
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-10
    Jérémie Joudioux

    The purpose of this note is to prove the existence of a conformal scattering operator for the cubic defocusing wave equation on a non-stationary background. The proof essentially relies on solving the characteristic initial value problem by the method developed by Hörmander. This method consists in slowing down the propagation speed of the waves to transform a characteristic initial value problem into

    更新日期:2020-03-10
  • Frobenius manifolds and a new class of extended affine Weyl groups of A-type
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-09
    Dafeng Zuo

    We present a new class of extended affine Weyl groups \(\widetilde{W}^{(k,k+1)}(A_l)\) for \(1\le k

    更新日期:2020-03-09
  • Frobenius objects in the category of relations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-07
    Rajan Amit Mehta, Ruoqi Zhang

    We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain

    更新日期:2020-03-07
  • Classical limits of gauge-invariant states and the choice of algebra for strict quantization
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-05
    Thomas L. Browning, Benjamin H. Feintzeig

    We analyze the quantization of a system consisting of a particle in an external Yang–Mills field within a C*-algebraic framework. We show that in both the classical and quantum theories of such a system, the kinematical algebra of physical quantities can be obtained by restricting attention to symmetry-invariant states on a C*-algebra. We use this to show that symmetry-invariant quantum states correspond

    更新日期:2020-03-05
  • Fock representations of ZF algebras and R -matrices
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-05
    Gandalf Lechner, Charley Scotford

    A variation of the Zamolodchikov–Faddeev algebra over a finite-dimensional Hilbert space \({\mathcal {H}}\) and an involutive unitary R-Matrix S is studied. This algebra carries a natural vacuum state, and the corresponding Fock representation spaces \({\mathcal {F}}_S({\mathcal {H}})\) are shown to satisfy \({\mathcal {F}}_{S\boxplus R}({{\mathcal {H}}}\oplus {{\mathcal {K}}}) \cong {\mathcal {F}}_S({{\mathcal

    更新日期:2020-03-05
  • Quillen metrics and perturbed equations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-05
    Vamsi Pritham Pingali

    We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations—the generalised Monge–Ampère equation, the almost Hitchin system, and the Calabi–Yang–Mills equations. These are all perturbations of already existing equations. Our construction for the generalised Monge–Ampère equation is conditioned on a conjecture from algebraic geometry

    更新日期:2020-03-05
  • n -Extended Lorentzian Kac–Moody algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-03-03
    Andreas Fring, Samuel Whittington

    We investigate a class of Kac–Moody algebras previously not considered. We refer to them as n-extended Lorentzian Kac–Moody algebras defined by their Dynkin diagrams through the connection of an \(A_n\) Dynkin diagram to the node corresponding to the affine root. The cases \(n=1\) and \(n=2\) correspond to the well-studied over- and very-extended Kac–Moody algebras, respectively, of which the particular

    更新日期:2020-03-03
  • Quadratic open quantum harmonic oscillator
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-28
    Ameur Dhahri, Franco Fagnola, Hyun Jae Yoo

    We study the quantum open system evolution described by a Gorini–Kossakowski–Sudarshan–Lindblad generator with creation and annihilation operators arising in Fock representations of the \(\mathfrak {sl}_2\) Lie algebra. We show that any initial density matrix evolves to a fully supported density matrix and converges towards a unique equilibrium state. We show that the convergence is exponentially fast

    更新日期:2020-02-28
  • Solutions of super Knizhnik–Zamolodchikov equations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-28
    Bintao Cao, Ngau Lam

    We establish an explicit bijection between the sets of singular solutions of the (super) KZ equations associated with the Lie superalgebra, of infinite rank, of type \(\mathfrak {a}, \mathfrak {b},\mathfrak {c},\mathfrak {d}\) and with the corresponding Lie algebra. As a consequence, the singular solutions of the super KZ equations associated with the classical Lie superalgebra, of finite rank, of

    更新日期:2020-02-28
  • Decay of Maxwell fields on Reissner–Nordström–de Sitter black holes
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-27
    Mokdad Mokdad

    In this paper we use Morawetz and geometric energy estimates—the so-called vector field method—to prove decay results for the Maxwell field in the static exterior region of the Reissner–Nordström–de Sitter black hole. We prove two types of decay: the first is a uniform decay of the energy of the Maxwell field on achronal hypersurfaces as the hypersurfaces approach timelike infinities. The second decay

    更新日期:2020-02-27
  • Long-time large-distance asymptotics of the transverse correlation functions of the XX chain in the spacelike regime
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-27
    Frank Göhmann, Karol K. Kozlowski, Junji Suzuki

    We derive an explicit expression for the leading term in the long-time, large-distance asymptotic expansion of a transverse dynamical two-point function of the XX chain in the spacelike regime. This expression is valid for all nonzero finite temperatures and for all magnetic fields below the saturation threshold. It is obtained here by means of a straightforward term-by-term analysis of a thermal form

    更新日期:2020-02-27
  • The notion of observable and the moment problem for $$*$$∗ -algebras and their GNS representations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-26
    Nicolò Drago, Valter Moretti

    We address some usually overlooked issues concerning the use of \(*\)-algebras in quantum theory and their physical interpretation. If \({\mathfrak {A}}\) is a \(*\)-algebra describing a quantum system and \(\omega : {\mathfrak {A}}\rightarrow {\mathbb {C}}\) a state, we focus, in particular, on the interpretation of \(\omega (a)\) as expectation value for an algebraic observable \(a=a^*\in {\mathfrak

    更新日期:2020-02-26
  • Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-21
    Philippe Mathieu, Laura Murray, Alexander Schenkel, Nicholas J. Teh

    We provide an elegant homological construction of the extended phase space for linear Yang–Mills theory on an oriented and time-oriented Lorentzian manifold M with a time-like boundary \(\partial M\) that was proposed by Donnelly and Freidel (JHEP 1609:102, 2016). This explains and formalizes many of the rather ad hoc constructions for edge modes appearing in the theoretical physics literature. Our

    更新日期:2020-02-21
  • A unifying 2D action for integrable $$\sigma $$σ -models from 4D Chern–Simons theory
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-15
    Francois Delduc, Sylvain Lacroix, Marc Magro, Benoît Vicedo

    In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable \(\sigma \)-models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the \(\lambda \)-deformation of the principal

    更新日期:2020-02-15
  • The star product in interacting quantum field theory
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-15
    Eli Hawkins, Kasia Rejzner

    We propose a new formula for the star product in deformation quantization of Poisson structures related in a specific way to a variational problem for a function S, interpreted as the action functional. Our approach is motivated by perturbative algebraic quantum field theory (pAQFT). We provide a direct combinatorial formula for the star product, and we show that it can be applied to a certain class

    更新日期:2020-02-15
  • Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-14
    Louis Ioos

    We use the theory of Berezin–Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows over closed prequantized symplectic manifolds in the context of geometric quantization of Kostant and Souriau. We express the associated evolution operators via parallel transport in the quantum spaces over the induced path of almost complex structures

    更新日期:2020-02-14
  • Pfaffian identities and Virasoro operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-14
    Kazuya Aokage, Eriko Shinkawa, Hiro-Fumi Yamada

    A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition \(\lambda =(\lambda _1,\lambda _2,\ldots ,\lambda _{2m})\), we show that, for \(k\ge 1\), \(L_{k}Q_{\lambda } = \sum ^{2m}_{i= 1}(\lambda _i-k)Q_{\lambda -2k\epsilon _i}\), where \(L_k\) is the Virasoro operator given as the quadratic form of free bosons. This main formula follows

    更新日期:2020-02-14
  • On localized and coherent states on some new fuzzy spheres
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-10
    Gaetano Fiore, Francesco Pisacane

    We construct various systems of coherent states (SCS) on the O(D)-equivariant fuzzy spheres \(S^d_\Lambda \) (\(d=1,2\), \(D=d+1\)) constructed in Fiore and Pisacane (J Geom Phys 132:423–451, 2018) and study their localizations in configuration space as well as angular momentum space. These localizations are best expressed through the O(D)-invariant square space and angular momentum uncertainties \((\Delta

    更新日期:2020-02-10
  • Quantum dimensions and irreducible modules of some diagonal coset vertex operator algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-02-06
    Xingjun Lin

    In this paper, under the assumption that the diagonal coset vertex operator algebra \(C(L_{\mathfrak {g}}(k+l,0),L_{\mathfrak {g}}(k,0)\otimes L_{\mathfrak {g}}(l,0))\) is rational and \(C_2\)-cofinite, the global dimension of \(C(L_{\mathfrak {g}}(k+l,0),L_{\mathfrak {g}}(k,0)\otimes L_{\mathfrak {g}}(l,0))\) is obtained and the quantum dimensions of multiplicity spaces viewed as \(C(L_{\mathfrak

    更新日期:2020-02-06
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