Existence of separable Fock Hilbert spaces for background-independent non-perturbative quantization of general relativity.
Projective Techniques and Functional Integration
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abstract
A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular prior knowledge of projective techniques is not assumed. (For the special JMP issue on Functional Integration, edited by C. DeWitt-Morette.)
fields
gr-qc 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Existence of background-independent Fock representations for canonical quantum gravity with matter, producing a separable Hilbert space unlike LQG.
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Non-perturbative, background independent Fock representations for canonical quantum gravity
Existence of separable Fock Hilbert spaces for background-independent non-perturbative quantization of general relativity.
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Non-perturbative, background independent canonical quantum gravity in Fock representations
Existence of background-independent Fock representations for canonical quantum gravity with matter, producing a separable Hilbert space unlike LQG.