Thiemann T (2024)
Publication Type: Journal article
Publication year: 2024
Book Volume: 110
Article Number: 124023
Journal Issue: 12
DOI: 10.1103/PhysRevD.110.124023
Perturbative quantum gravity starts from prescribing a background metric. That background metric is then used in order to carry out two separate steps: 1. One splits the nonperturbative metric into background and deviation from it (graviton) and expands the action in terms of the graviton which results in an infinite series of unknown radius of convergence. 2. One constructs a Fock representation for the graviton and performs perturbative graviton quantum field theory on the fixed background as dictated by the perturbative action. The result is a nonrenormalizable theory without predictive power. It is therefore widely believed that a nonperturbative approach is mandatory in order to construct a fundamental, not only effective, predictive quantum field theory of the gravitational interaction. Since perturbation theory is by definition background dependent, the notions of background dependence (BD) and perturbation theory (PT) are often considered as symbiotic, as if they imply each other. In the present work, we point out that there is no such symbiosis; these two notions are in fact logically independent. In particular, one can use BD structures while not using PT at all. Specifically, we construct BD Fock representations (step 2 above) for the full, nonperturbative metric rather than the graviton (not step 1 above) and therefore never perform a perturbative expansion. Despite the fact that the gravitational Lagrangian is a nonpolynomial, not even analytic, function of the metric, we show that, e.g., the Hamiltonian constraint with any density weight can be defined as a quadratic form with dense form domain in such a representation.
APA:
Thiemann, T. (2024). Nonperturbative quantum gravity in Fock representations. Physical Review D, 110(12). https://doi.org/10.1103/PhysRevD.110.124023
MLA:
Thiemann, Thomas. "Nonperturbative quantum gravity in Fock representations." Physical Review D 110.12 (2024).
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