2024-03-08   63548

Scalar Quantum Fields on a Spacetime Lattice

This article introduces the path integral formulation of quantum field theory for scalar quantum fields, treating spacetime as a (very fine) lattice to make the whole construction mathematically unambiguous. In this formulation, time evolution is expressed in terms of an action (the integral of a lagrangian) that has a manifestly Lorentz symmetric continuum limit. This can be viewed as the quantum version of the action principle. Starting with the path integral formulation, this article explains how to recover the hamiltonian formulation that was used in article 52890, including the equal-time commutation relations.

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www.cphysics.org updated 2024-04-08