Mechanization of scalar field theory in 1+1 dimensions

TL;DR

This paper introduces a method called 'mechanization' that approximates scalar field theories in 1+1 dimensions using piece-wise linear functions, enabling the study of complex dynamical phenomena through manageable mechanical models.

Contribution

It presents a novel approximation technique transforming scalar fields into finite graph-based models, revealing emergent dynamical objects and phenomena as the model complexity increases.

Findings

Emergence of mech-kinks and mech-oscillons in simple models

Observation of bouncing phenomena and bion pair-production in complex models

Gradual development of intricate dynamical patterns with increasing N

Abstract

The `mechanization' is a procedure of replacing a scalar field in 1+1 dimensions with a piece-wise linear function, i.e. a finite graph consisting of $N$ joints (vertices) and straight segments (edges). As a result, the field theory is approximated by a sequence of algebraically tractable, general-purpose collective coordinate mechanical models. We observe the step-by-step emergence of dynamical objects and associated phenomena as the $N$ increases. Mech-kinks and mech-oscillons -- mechanical analogs of kinks and oscillons (bions) -- appear in the simplest models, while more intricate dynamical patterns, such as bouncing phenomenon and bion pair-production, emerge gradually as decay states of high $N$ mech-oscillons.