Prog. Theor. Phys. Supplement No.164 (2006) pp. 68-81
Dirac Sea for Bosons Also and SUSY for Single Particles
1Department of Physics, Osaka University, Osaka 560-0043, Japan
2Niels Bohr Institute, University Copenhagen, 17 Blegdamsvej
Copenhagen ø, Denmark
3Yukawa Institute for Theoretical Physics, Kyoto University,
Kyoto 606-8502, Japan
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.
DOI : 10.1143/PTPS.164.68
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