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  • Aharonov–Bohm superselection sectors
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-17
    Claudio Dappiaggi, Giuseppe Ruzzi, Ezio Vasselli

    We show that the Aharonov–Bohm effect finds a natural description in the setting of QFT on curved spacetimes in terms of superselection sectors of local observables. The extension of the analysis of superselection sectors from Minkowski spacetime to an arbitrary globally hyperbolic spacetime unveils the presence of a new quantum number labelling charged superselection sectors. In the present paper

    更新日期:2020-10-17
  • Formal power series for asymptotically hyperbolic Bach-flat metrics
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-13
    Aghil Alaee, Eric Woolgar

    It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein 4-metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian setting. Following an approach pioneered by Fefferman and Graham for the Einstein equation, we find formal power series for conformally compactifiable, asymptotically

    更新日期:2020-10-13
  • A Lorentz-covariant interacting electron–photon system in one space dimension
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-08
    Michael K.-H. Kiessling, Matthias Lienert, A. Shadi Tahvildar-Zadeh

    A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions \(\Psi ^{{(2)}}(\mathbf {x}_{\text{ ph }},\mathbf {x}_{\text{ el }})\) where \(\mathbf {x}_{\text{ el }},\mathbf {x}_{\text{

    更新日期:2020-10-08
  • An operational construction of the sum of two non-commuting observables in quantum theory and related constructions
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-04
    Nicolò Drago, Sonia Mazzucchi, Valter Moretti

    The existence of a real linear space structure on the set of observables of a quantum system—i.e., the requirement that the linear combination of two generally non-commuting observables A, B is an observable as well—is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable

    更新日期:2020-10-04
  • Bulk-boundary asymptotic equivalence of two strict deformation quantizations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-10-01
    Valter Moretti, Christiaan J. F. van de Ven

    The existence of a strict deformation quantization of \(X_k=S(M_k({\mathbb {C}}))\), the state space of the \(k\times k\) matrices \(M_k({\mathbb {C}})\) which is canonically a compact Poisson manifold (with stratified boundary), has recently been proved by both authors and Landsman (Rev Math Phys 32:2050031, 2020. https://doi.org/10.1142/S0129055X20500312). In fact, since increasing tensor powers

    更新日期:2020-10-02
  • Duality for Bethe algebras acting on polynomials in anticommuting variables
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-13
    V. Tarasov, F. Uvarov

    We consider actions of the current Lie algebras \(\mathfrak {gl}_{n}[t]\) and \(\mathfrak {gl}_{k}[t]\) on the space of polynomials in kn anticommuting variables. The actions depend on parameters \(\bar{z}=(z_{1},\dots ,z_{k})\) and \({\bar{\alpha }}=(\alpha _{1},\dots ,\alpha _{n})\), respectively. We show that the images of the Bethe algebras \(\mathcal {B}_{{\bar{\alpha }}}^{\langle n \rangle }\subset

    更新日期:2020-09-13
  • An optimal semiclassical bound on commutators of spectral projections with position and momentum operators
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-08
    Søren Fournais, Søren Mikkelsen

    We prove an optimal semiclassical bound on the trace norm of the following commutators \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),x]\), \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),-i\hbar \nabla ]\) and \([{\varvec{1}}_{(-\infty ,0]}(H_\hbar ),e^{i\langle t, x\rangle }]\), where \(H_\hbar \) is a Schrödinger operator with a semiclassical parameter \(\hbar \), x is the position operator, \(-\,i\hbar \nabla

    更新日期:2020-09-08
  • Full colored HOMFLYPT invariants, composite invariants and congruence skein relations
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-09-07
    Qingtao Chen, Shengmao Zhu

    In this paper, we investigate the properties of certain quantum invariants of links by using the HOMFLY skein theory. First, we obtain the limit behavior for the full colored HOMFLYPT invariant which is the natural generalization of the colored HOMFLYPT invariant. Then we focus on the composite invariant which is a certain combination of the full colored HOMFLYPT invariants. Motivated by the study

    更新日期:2020-09-08
  • Correction to: Solving q -Virasoro constraints
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-31
    Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov, Maxim Zabzine

    The publication of this article unfortunately contained a mistake. One affiliation of the author Shamil Shakirow was missing; you can find the corrected affiliations above.

    更新日期:2020-09-01
  • Tropical limit of matrix solitons and entwining Yang–Baxter maps
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-11
    Aristophanes Dimakis, Folkert Müller-Hoissen

    We consider a matrix refactorization problem, i.e., a “Lax representation,” for the Yang–Baxter map that originated as the map of polarizations from the “pure” 2-soliton solution of a matrix KP equation. Using the Lax matrix and its inverse, a related refactorization problem determines another map, which is not a solution of the Yang–Baxter equation, but satisfies a mixed version of the Yang–Baxter

    更新日期:2020-08-12
  • Approximation of one-dimensional relativistic point interactions by regular potentials revised
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-12
    Matěj Tušek

    We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form \(1/\varepsilon ~h(x/\varepsilon )\otimes B\), where B is a suitable \(2\times 2\) matrix. Moreover, we prove that the limit does not depend on the particular choice of h as long as it integrates to a constant

    更新日期:2020-08-12
  • Infinity-enhancing of Leibniz algebras
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-11
    Sylvain Lavau, Jakob Palmkvist

    We establish a correspondence between infinity-enhanced Leibniz algebras, recently introduced in order to encode tensor hierarchies (Bonezzi and Hohm in Commun Math Phys 377:2027–2077, 2020), and differential graded Lie algebras, which have been already used in this context. We explain how any Leibniz algebra gives rise to a differential graded Lie algebra with a corresponding infinity-enhanced Leibniz

    更新日期:2020-08-11
  • On the Hamiltonian formulation of the trigonometric spin Ruijsenaars–Schneider system
    Lett. Math. Phys. (IF 1.371) Pub Date : 2020-08-10
    Oleg Chalykh, Maxime Fairon

    We suggest a Hamiltonian formulation for the spin Ruijsenaars–Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a representation space of a framed Jordan quiver. For arbitrary quivers, analogous varieties were introduced by Crawley-Boevey and Shaw, and their interpretation as quasi-Hamiltonian

    更新日期:2020-08-11
  • 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
  • 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
  • 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:2020-08-03
  • 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:2020-07-27
  • 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
  • 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
  • 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:2020-06-30
  • 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:2020-06-20
  • 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
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