On the Two-Point Correlation Function in Dynamical Scaling and SCHR\"Odinger Invariance

TL;DR

This paper explores how Schr"odinger invariance fully determines the two-point correlation function in systems with dynamical scaling, extending to local space-time transformations, and verifies the results in exactly solvable models.

Contribution

It demonstrates that Schr"odinger invariance uniquely constrains the two-point correlation function for systems with dynamical exponent z=2, extending the understanding of local scale invariance.

Findings

Schr"odinger invariance fully determines the two-point correlation function.

Verification in two exactly solvable models confirms the theoretical predictions.

Extension of dynamical scaling to local space-time transformations is achieved.

Abstract

The extension of dynamical scaling to local, space-time dependent rescaling factors is investigated. For a dynamical exponent $z=2$, the corresponding invariance group is the Schr\"odinger group. Schr\"odinger invariance is shown to determine completely the two-point correlation function. The result is checked in two exactly solvable models.