(Received December 7, 2004)
We propose the formulation of a second quantization of a bosonic
theory by generalizing the method of filling the Dirac negative energy
sea for the case of fermions.
We interpret our results as implying that the correct vacuum for the
bosonic theory is
obtained by adding minus one boson to each single particle negative
energy state while the positive energy states are empty.
The boson states are divided into two sectors:
the usual positive sector consisting of states with a positive (or
zero) number of bosons, and
the negative sector,consisting of states with a negative number of bosons.
Once a state enters the negative sector, it cannot return to the usual
positive sector through an ordinary interaction, due to the presence
of a barrier.
To study this problem, a toy model, in which the filling of the empty fermion Dirac sea and the removal of bosons from the negative energy states has not yet been performed, has been proposed. We put forward such a naive vacuum world in the present paper. A subsequent paper [hep-th/0410218] will treat various properties: the analyticity of the wave functions, the interaction and a CPT-like theorem in the naive vacuum world.
URL : http://ptp.ipap.jp/link?PTP/113/603/
DOI : 10.1143/PTP.113.603
*Also, Okayama Institute for Quantum Physics, Okayama 700-0015, Japan.