Quantum field theory on a growing lattice

TL;DR

The paper addresses how to formulate quantum field theory on a background lattice whose number of points grows in time, a proxy for a growing spacetime with a fixed microscopic structure. It develops an algebraic, Hamiltonian framework with a conserved symplectic form and a phase space of half-solutions to accommodate mode birth, and it demonstrates the construction via a hyperdiamond lattice with a Fock-space representation. In a 1+1D example, growth-induced birth of modes injects substantial energy into the vacuum, suggesting that mode birth on a background lattice may be incompatible with observed cosmology unless new dynamics (e.g., dynamical spacetime) are invoked. The work thereby clarifies both the mathematical structure needed to treat growing lattices and the substantial physical obstacles such models face, while pointing toward potential connections with quantum gravity approaches that treat spacetime itself dynamically.

Abstract

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.