Optics, Mechanics and Quantization of Reparametrization Systems

Details Optics, Mechanics and Quantization of Reparametrization Systems Optics, Mechanics and Quantization of Reparametrization Systems

1994-04-20

arxiv.org/abs/hep-th/9404121v1

J.Math.Phys. 35 (1994) 6407-6417

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, Latex

Scientific paper

10.1063/1.530682

In this paper we regard the dynamics obtained from Fermat principle as begin the classical theory of light. We (first-)quantize the action and show how close we can get to the Maxwell theory. We show that Quantum Geometric Optics is not a theory of fields in curved space. Considering Classical Mechanics to be on the same footing, we show the parallelism between Quantum Mechanics and Quantum Geometric Optics. We show that, due to the reparametrization invariance of the classical theories, the dynamics of the quantum theories is given by a Hamiltonian constraint. Some implications of the above analogy in the quantization of true reparameterization invariant systems are discussed.

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