Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum

TL;DR

This paper develops a supersymmetric quantum field theory incorporating a deformed Heisenberg algebra that accounts for minimal length and maximal momentum, extending traditional frameworks with novel algebraic structures.

Contribution

It introduces a deformed supersymmetric algebra based on a modified Heisenberg algebra, integrating minimal length and maximal momentum into supersymmetric quantum theories.

Findings

Constructed a supersymmetric quantum theory with deformed algebra.

Derived a deformed supersymmetric algebra considering minimal length and maximal momentum.

Provides a framework for exploring quantum theories with fundamental length scales.

Abstract

We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra $[x,p]=i\hbar\big(1-\beta p+2\beta^{2}p^{2}\big)$, where $\beta $ is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.