Multisymplectic effective General Boundary Field Theory

Abstract

The transfer matrix in lattice field theory connects the covariant and the initial data frameworks; in spin foam models, it can be written as a composition of elementary cellular amplitudes/propagators. We present a framework for discrete spacetime classical field theory in which solutions to the field equations over elementary spacetime cells may be amalgamated if they satisfy simple gluing conditions matching the composition rules of cellular amplitudes in spin foam models. Furthermore, the formalism is endowed with a multisymplectic structure responsible for local conservation laws. Some models within our framework are effective theories modeling a system at a given scale. Our framework allows us to study coarse graining and the continuum limit.

References in corpus (3)

• Perfect discretization of reparametrization invariant path integrals
• Plebanski gravity without the simplicity constraints
• Uniform discretizations: a quantization procedure for totally constrained systems including gravity

Cited by in corpus (5)

• Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
• Classification of constraints and degrees of freedom for quadratic discrete actions
• Covariant Momentum Map Thermodynamics for Parametrized Field Theories
• Observable currents in lattice field theories
• Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs