Propagators in the continuum limit: from molecules to scalar fields

TL;DR

This paper derives the propagator for large molecules and continuum limits, connecting molecular models to scalar field theories and analyzing their quantum evolution and responses to perturbations.

Contribution

It provides a novel approximation for the propagator of large N molecules and explores their continuum limit, linking molecular dynamics to quantum field theory.

Findings

Closed-form propagator for N ≤ 4 molecules

Approximate propagator for N >> 1 molecules

Analysis of scalar field quantization and perturbations

Abstract

The propagator of linear molecules whose constituents interact through oscillator potentials can be obtained in a closed form for $N$ atoms as long as $N \leq 4$. We compute the propagator for arbitrary $N$ in the approximation $N \gg 1$. Taking advantage of this result it is possible to analyze the limit in which the molecule has an infinite number of constituents with infinitesimal length of sepparation, corresponding to the quantization of a string, elastic rod or the second quantization of a Klein Gordon particle. The evolution of some specific initial conditions is also studied, namely the time development of states with minimal dispersion and the effect of sudden perturbations on the vacuum of the scalar field theory.