标题： 广义哈密顿空间：新发展和应用 显示英文标题

标题： Generalized Hamilton spaces: new developments and applications

摘要： 在本工作中，我们对依赖于所有相空间变量的通用余切丛几何进行了新的发展。 特别是，我们将关注所谓的广义哈密顿空间，讨论这种几何框架的主要成分，如哈密顿量和非线性及仿射联络，如何从给定度规中导出。 展示了这类空间的一些性质，针对测地线哈密顿量。 此外，我们研究了度规的时空和动量等距性。 最后，我们讨论了余切丛几何在量子引力中的可能应用，例如变形相对论运动学和非对易时空的构建。 显示英文摘要

摘要： In this work, we make 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 are 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.