Dirac Sea and Hole Theory for Bosons I -- A new formulation of quantum field theories --

TL;DR

This paper introduces a novel bosonic Dirac sea and hole theory formulation, extending the fermionic concept to bosons, ensuring positive probabilities and applicability to supersymmetric and string theories.

Contribution

It presents a consistent bosonic Dirac sea and hole theory, including a double harmonic oscillator method, applicable to supersymmetric and string theories.

Findings

Bosonic vacuum modeled as a negative energy sea.

Positive definite physical probabilities achieved.

Applicable to supersymmetric and string theories.

Abstract

Bosonic formulation of the negative energy sea, so called Dirac sea, is proposed by constructing a hole theory for bosons as a new formulation of the second quantization of bosonic fields. The original idea of Dirac sea for fermions, where the vacuum state is considered as a state completely filled by fermions of negative energy and holes in the sea are identified as anti-particles, is extended to boson case in a consistent manner. The bosonic vacuum consists of a sea filled by negative energy bosonic states, while physical probabilities become always positive definite. We introduce a method of the double harmonic oscillator to formulate the hole theory of bosons. Our formulation is also applicable to supersymmetric field theory. The sea for supersymmetric theories has an explicit supersymmetry. We suggest applications of our formulations to the anomaly theories and the string theories.