Annals of Physics ( IF 3 ) Pub Date : 2021-05-13 , DOI: 10.1016/j.aop.2021.168507 Alejandro Aguilar-Salas , Efraín Rojas
We develop a constructive procedure for arriving at the Hamilton–Jacobi framework for the so-called affine in acceleration theories by analysing the canonical constraint structure. We find two scenarios in dependence of the order of the emerging equations of motion. By properly defining generalized brackets, the non-involutive constraints that originally arose, in both scenarios, may be removed so that the resulting involutive Hamiltonian constraints ensure integrability of the theories and, at the same time, lead to the right dynamics in the reduced phase space. In particular, when we have second-order derivatives equations of motion we are able to detect the gauge invariant sector of the theory by using a suitable approach based on the projection of the Hamiltonians onto the tangential and normal directions of the congruence of curves in the configuration space. Regarding this, we also explore the generators of canonical and gauge transformations of these theories. Further, we briefly outline how to determine the Hamilton principal function for some particular setups. We apply our findings to some representative theories: a Chern–Simons-like theory in -dim, an harmonic oscillator in and, the geodetic brane cosmology emerging in the context of extra dimensions.
中文翻译:
依赖于线性加速度的拉格朗日函数的Hamilton–Jacobi方法
通过分析规范约束结构,我们为推论加速理论中的所谓仿射建立了一种构造性的程序,以建立汉密尔顿-雅各比框架。我们发现了两种情况,它们与新兴的运动方程式的顺序有关。通过正确定义广义括号,可以消除在两种情况下最初出现的非对合约束,从而使所产生的对合哈密顿约束可以确保理论的可集成性,并同时在简化阶段提供正确的动力。空间。特别是,当我们具有运动的二阶导数方程时,我们能够使用合适的方法,基于哈密顿量在构形空间中曲线的全切线的切线方向和法线方向上的投影,来检测该理论的规范不变扇区。关于这一点,我们还将探讨这些理论的规范和规范转换的产生者。此外,我们简要概述了如何确定汉密尔顿主函数对于某些特定的设置。我们将我们的发现应用于一些代表性理论:-dim,一个谐波振荡器 并且,大地尺度的宇宙学在额外的维度中出现。