A relational Hamiltonian for group field theory

Abstract

Using a massless scalar field as a clock variable, the Legendre transform of the 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 family of states are condensates, as they are expected to correspond to the cosmological sector of group field theory. For the relational Hamiltonian considered in this paper, the coarse-grained dynamics of a simple type 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.

11 pages. v2: Clarifications added, typos corrected and references added

References in corpus (7)

• Quantum Nature of the Big Bang: Improved dynamics
• LQG vertex with finite Immirzi parameter
• Gravity quantized
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity

Cited by in corpus (28)

• Group field theory condensate cosmology: An appetizer
• Effective relational cosmological dynamics from Quantum Gravity
• Inhomogeneous universe from group field theory condensate
• Generalised effective cosmology from group field theory
• Quantum fluctuations in the effective relational GFT cosmology
• Thermal quantum gravity condensates in group field theory cosmology
• Hamiltonian group field theory with multiple scalar matter fields
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Limiting curvature mimetic gravity for group field theory condensates
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Loop quantum cosmology: relation between theory and observations
• Frozen formalism and canonical quantization in group field theory
• Addendum to "Relational Hamiltonian for group field theory"
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Towards anisotropic cosmology in group field theory
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Stochastic dynamics for Group Field Theories
• Relational dynamics and Page-Wootters formalism in group field theory
• Stationary cosmology in group field theory
• Gauge-invariant perturbations at a quantum gravity bounce
• Hilbert space formalisms for group field theory
• Foundational Issues in Group Field Theory
• Reconstructing the metric in group field theory
• Thermofield Double States in Group Field Theory
• Cosmological implications of the hydrodynamical phase of group field theory
• Relational Time as a Stochastic Variable in ADM Gravity
• Effective cosmology from one-body operators in group field theory