An Alternative Dimensional Reduction Prescription

TL;DR

This paper introduces a new method for dimensional reduction that preserves interaction structures and dynamics, with applications to scalars, fermions, bosonization, and supersymmetry in two dimensions.

Contribution

It presents an alternative dimensional reduction approach that maintains the form of interactions, offering a more physical reduction method compared to traditional techniques.

Findings

Preserves interaction structures in reduced models

Constructs reduced Lagrangians for scalars and fermions

Discusses bosonization and supersymmetry in 2D

Abstract

We propose an alternative dimensional reduction prescription which in respect with Green functions corresponds to drop the extra spatial coordinate. From this, we construct the dimensionally reduced Lagrangians both for scalars and fermions, discussing bosonization and supersymmetry in the particular 2-dimensional case. We argue that our proposal is in some situations more physical, in the sense that it mantains the form of the interactions between particles, thus preserving the dynamics corresponding to the higher dimensional space.