Hamiltonian quantization of General Relativity with the change of signature

Details Hamiltonian quantization of General Relativity with the change of signature Hamiltonian quantization of General Relativity with the change of signature

1994-02-15

arxiv.org/abs/gr-qc/9402028v1

Phys.Rev.D49:5086-5095,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages, GCR-93/11/01, To appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.49.5086

We show in this article how the usual hamiltonian formalism of General Relativity should be modified in order to allow the inclusion of the Euclidean classical solutions of Einstein's equations. We study the effect that the dynamical change of signature has on the superspace and we prove that it induces a passage of the signature of the supermetric from ($-+++++$) to ($+-----$). Next, all these features are more particularly studied on the example of minisuperspaces. Finally, we consider the problem of quantization of the Euclidean solutions. The consequences of different choices of boundary conditions are examined.

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