Slab Bag Fermionic Casimir effect, Chiral Boundaries and Vector Boson - Majorana Fermion Pistons

TL;DR

This paper investigates the Casimir effect for Majorana fermions and vector bosons with various boundary conditions, revealing a new regularization mechanism and exploring supersymmetry's role in energy cancellation.

Contribution

It introduces a novel regularization approach at the energy density level and analyzes boundary broken supersymmetry effects in fermion-boson systems.

Findings

Regularization occurs explicitly at the Casimir energy density.

Boundary broken supersymmetry explains field multiplicities.

Casimir energy can vanish with specific boundary conditions.

Abstract

In this article we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We present a new regularization mechanism the piston offers. In our case regularization occurs explicitly at the Casimir energy density and not at the Casimir force level, as in usual pistons. We make use of boundary broken supersymmetry to explain the number of fields that appear in all the studied cases. The effect of chiral boundary conditions in a fermion boson system is investigated. Concerning the supersymmetry issue and the vanishing Casimir energy, we study a massive Dirac fermion-scalar boson system with bag and specific Robin type boundary conditions for which the Casimir energy vanishes. Finally a two scalar bosons system between parallel plates is presented in which the singularities vanish in the total Casimir energy. A discussion on boundary broken supersymmetry follows.