Boson Sea versus Dirac Sea -- General formulation of boson sea through supersymmetry --

TL;DR

This paper proposes a formalism for a boson sea analogous to the Dirac sea for fermions, using supersymmetry and a double harmonic oscillator approach, to address longstanding issues in bosonic vacuum structure.

Contribution

It introduces a novel formalism for boson vacua based on supersymmetry and double harmonic oscillators, extending the Dirac sea concept to bosons.

Findings

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

Hole creation in the boson sea corresponds to anti-particles.

Method aligns with standard second quantization results.

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. Here, we must admit that it is only possible if we allow --as occurs in the usual formalism anyway-- that the "Hilbert space" for the single particle bosons is not positive definite. 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. This double harmonic oscillator includes not only positive energy states but also negative energy states. We utilize this method to construct a general formalism for a boson sea analogous to the Dirac sea, irrespective of the existence of supersymmetry. The physical result is consistent with that of the ordinary second quantization formalism. We finally suggest applications of our method to the string theories.