Generalized Hamilton spaces: New developments and applications

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-08-19 DOI:10.1016/j.geomphys.2025.105626

J.J. Relancio , L. Santamaría-Sanz

引用次数: 0

Abstract

In this work, we present new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this geometrical framework, such as the Hamiltonian and the nonlinear and affine connections, can be derived from a given metric. Several properties of this kind of spaces have been demonstrated for autoparallel Hamiltonians. Moreover, we study the spacetime and momentum isometries of the metric. Finally, we discuss the possible applications of cotangent bundle geometries in quantum gravity, such as the construction of deformed relativistic kinematics and non-commutative spacetimes.

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广义汉密尔顿空间：新发展与应用

在这项工作中，我们提出了依赖于所有相空间变量的一般共切束几何的新进展。特别地，我们将关注所谓的广义汉密尔顿空间，讨论这个几何框架的主要成分，如哈密顿量和非线性和仿射连接，如何从给定的度量中推导出来。对于自平行哈密顿量，已经证明了这类空间的几个性质。此外，我们还研究了度规的时空和动量等距。最后，我们讨论了余切束几何在量子引力中的可能应用，如变形相对论运动学和非交换时空的构造。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity