Dirac Sea for Bosons

Abstract

It is proposed to make formulation of second quantizing a bosonic theory by generalizing the method of filling the Dirac negative energy sea for fermions. We interpret that the correct vacuum for the bosonic theory is obtained by adding minus one boson to each single particle negative energy states while the positive energy states are empty. The boson states are divided into two sectors ; the usual positive sector with positive and zero numbers of bosons and the negative sector with negative numbers of bosons. Once it comes into the negative sector it cannot return to the usual positive sector by ordinary interaction due to a barrier. It is suggested to use as a playround models in which the filling of empty fermion Dirac sea and the removal of boson from the negative energy states are not yet performed. We put forward such a naive vacuum world and propose a CPT-like theorem for it.We study it in detail and give a proof for $\lambda /4({\varphi }^{+}\varphi {)}^2$ theory. The CPT-like theorem is a strong reflection, but does not include inversion of operator order which is involved in the ordinary CPT theorem. Instead it needs certain analytic continuation of the multiple wave function when the state is formulated as a finite number of particles present.

39 pages, 1 figure, LaTeX

Cited by in corpus (5)

• Dirac Sea and Hole Theory for Bosons I -- A new formulation of quantum field theories --
• Stretching the electron as far as it will go
• The static PQCD potential with modified boundary conditions
• Dirac Sea and Hole Theory for Bosons II -- Renormalization Approach --
• Stochastic Mechanics Without Ad Hoc Quantization: Theory And Applications To Semiclassical Gravity