前辛几何与时间问题。第1部分
Presymplectic Geometry and the Problem of Time. Part 1
摘要：
基于前辛几何，提出了一个处理广义相对论中无时间动力学“相空间图像”的有效数学框架。在广义相对论中，消失的标量哈密顿约束的存在导致了时间问题，这个问题可以通过采用无时间的形式主义来解决。这已经由Carlo Rovelli和Julian Bartheland等人完成。在本文中，我们提出了Bartheland理论的相空间重构。发展了一般的全约束、重参数化不变量理论的前辛动力学，并将其应用于Jacobi力学、关系粒子力学和自由相对论粒子动力学。
英文摘要：
An effective mathematical framework based on Presymplectic Geometry for dealing with the "phase space picture" of timeless dynamics in General Relativity is presented. In General Relativity, the presence of the scalar Hamiltonian constraint which vanishes leads to the problem of time, which can be solved, up to an extent by adopting a timeless formalism. This has been done by Carlo Rovelli and Julian Barbour et al. In this paper we present a phase space reformulation of Barbour's theory. The Presymplectic dynamics of general totally constrained, reparametrization invariant theories is developed, then applied to Jacobi mechanics, relational particle mechanics and the dynamics of the free relativistic particle.
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