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Prog. Theor. Phys. Supplement No.164 (2006) pp. 68-81

[ Full Text PDF : FREE ACCESS (174K) ]

Dirac Sea for Bosons Also and SUSY for Single Particles

Yoshinobu Habara,1,* Holger B. Nielsen2 and Masao Ninomiya3,**

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

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. 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.


URL : http://ptp.ipap.jp/link?PTPS/164/68/
DOI : 10.1143/PTPS.164.68


*Adress after 1 April 2005, Department of Physics, Kyoto University, Kyoto 606-8502, Japan.
**Also working at Okayama Institute for Quantum Physics.

[ Full Text PDF : FREE ACCESS (174K) ] Citation:

References:

  1. P. A. M. Dirac, Proc. R. Soc. London A 126 (1930), 360; Proc. Cambridge Philos. Soc. 26 (1930), 361.
  2. S. Weinberg, The Quantum Theory of Fields, Volume I: Foundations (Cambridge University Press).
  3. H. B. Nielsen and M. Ninomiya, hep-th/9808108[e-print arXiv]; Prog. Theor. Phys. 113 (2005), 603[PTP]; hep-th/0410216[e-print arXiv]; Prog. Theor. Phys. 113 (2005), 625[PTP]; hep-th/0410218[e-print arXiv].
  4. Y. Habara, H. B. Nielsen and M. Ninomiya, Int. J. Mod. Phys. A 19 (2004), 5561; hep-th/0312302[e-print arXiv].
  5. Y. Habara, H. B. Nielsen and M. Ninomiya, hep-th/0504173[e-print arXiv].
  6. Y. Habara, H. B. Nielsen and M. Ninomiya, hep-th/0505237[e-print arXiv].
  7. M. F. Sohnius, Phys. Rep. 128 (1985), 39[CrossRef].
  8. P. West, Introduction to Supersymmetry and Supergravity (World Scientific).

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