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arXiv · 2312.10272

Covariant canonical quantization and the problem of time

S. Carlip·Weixuan Hu
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Abstract

In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be viewed as a coordinate change. We argue for a similar view in quantum theory. As in the Heisenberg picture, the wave function is fundamentally time-independent. On any given time slice, however, we can diagonalize a complete set of position operators to form a basis, in which the projected wave function depends on the choice of time. In this picture, time evolution can be viewed as a basis change in what is otherwise a block universe. We argue that this may help solve the ``problem of time'' in quantum gravity, and illustrate the idea with an example from three-dimensional quantum gravity.

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S. Carlip, Weixuan Hu. 2023-12-16. Covariant canonical quantization and the problem of time. https://arxiv.org/abs/2312.10272

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