Quantizing Regge calculus

Details Quantizing Regge calculus Quantizing Regge calculus

1995-12-21

arxiv.org/abs/gr-qc/9512040v1

Class.Quant.Grav. 13 (1996) 2385-2394

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, plain TeX, one postcript figure, uuencoded

Scientific paper

10.1088/0264-9381/13/9/006

A discretized version of canonical gravity in (3+1)-d introduced in a previous paper is further developed, introducing the Liouville form and the Poisson brackets, and studying them in detail in an explicit parametrization that shows the nature of the variables when the second class constraints are imposed. It is then shown that, even leaving aside the difficult question of imposing the first class constraints on the states, it is impossible to quantize the model directly, using complex variables and leaving the second class constraints to fix the metric of the quantum Hilbert, because one cannot find a metric which makes the area variables hermitean.

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