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#### Statistical Equilibrium in Quantum Gravity: Gibbs states in Group Field Theory

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1801.09964.pdf

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Kotecha_2018_New_J._Phys._20_073009.pdf

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##### Citation

Kotecha, I., & Oriti, D. (2018). Statistical Equilibrium in Quantum Gravity: Gibbs
states in Group Field Theory.* New Journal of Physics,* *20*:
073009. doi:10.1088/1367-2630/aacbbd.

Cite as: https://hdl.handle.net/21.11116/0000-0000-BA51-3

##### Abstract

Due to the absence of well-defined concepts of time and energy in background
independent systems, formulating statistical equilibrium in such settings
remains an open issue. Even more so in the full quantum gravity context, not
based on any of the usual spacetime notions but on non-spatiotemporal degrees
of freedom. In this paper, after having clarified different general notions of
statistical equilibrium, on which different construction procedures can be
based, we focus on the group field theory formalism for quantum gravity, whose
technical features prove advantageous to the task. We use the operatorial
formulation of group field theory to define its statistical mechanical
framework, and, based on this, we construct three concrete examples of Gibbs
states. The first is a Gibbs state with respect to a geometric volume operator,
which is shown to support condensation to a low-spin phase. This state is not
based on a pre-defined flow and its construction is via Jaynes' entropy
maximisation principle. The second are Gibbs states encoding structural
equilibrium with respect to internal translations on the GFT base manifold, and
defined via the KMS condition. The third are Gibbs states encoding relational
equilibrium with respect to a clock Hamiltonian, obtained by deparametrization
with respect to coupled scalar matter fields.