Dirac Sea for Bosons also and SUSY for Single Particles

TL;DR

This paper proposes that boson vacuums can be viewed as a sea of filled negative energy states, similar to fermions, using supersymmetry, and introduces a double harmonic oscillator concept.

Contribution

It introduces a novel boson sea concept analogous to the Dirac sea and explores supersymmetric relativistic quantum mechanics formulations.

Findings

Boson vacuum can be viewed as a filled negative energy sea.

Negative energy bosons' holes correspond to anti-particles.

A double harmonic oscillator formalism is proposed.

Abstract

We consider the long standing problem in field theories of bosons that the boson vacuum does not consist of a `sea', unlike the fermion vacuum. We show with the help of supersymmetry considerations that the boson vacuum indeed does also consist of a sea in which the negative energy states are all "filled", analogous to the Dirac sea of the fermion vacuum, and that a hole produced by the annihilation of one negative energy boson is an anti-particle. This might be formally coped with by introducing the notion of a double harmonic oscillator, which is obtained by extending the condition imposed on the wave function. Next, we present an attempt to formulate the supersymmetric and relativistic quantum mechanics utilizing the equations of motion.