Relational Hamiltonian for group field theory

Using a massless scalar field as a clock variable, the Legendre transform of a group field theory Lagrangian gives a relational Hamiltonian. In the classical theory, it is natural to define "equal relational time" Poisson brackets, where "equal time" corresponds to equal values o...

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Bibliographic Details
Published in:Physical review. D 2019-04, Vol.99 (8), p.1, Article 086017
Main Author: Wilson-Ewing, Edward
Format: Article
Language:English
Subjects:
Big bang cosmology
Brackets
Commutation
Condensates
Field theory
Quantum gravity
Quantum theory
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Summary:Using a massless scalar field as a clock variable, the Legendre transform of a group field theory Lagrangian gives a relational Hamiltonian. In the classical theory, it is natural to define "equal relational time" Poisson brackets, where "equal time" corresponds to equal values of the scalar field clock. The quantum theory can then be defined by imposing equal relational time commutation relations for the fundamental operators of the theory, with the states being elements of a Fock space with their evolution determined by the relational Hamiltonian operator. A particularly interesting type of states are condensates, as they may correspond to the cosmological sector of group field theory. For the relational Hamiltonian considered in this paper, the coarse-grained dynamics of a simple family of condensate states agree exactly with the Friedmann equations in the classical limit and also include quantum gravity corrections that ensure the big bang singularity is replaced by a bounce.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.99.086017