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Prog. Theor. Phys. Vol. 56 No. 6 (1976) pp. 1948-1964
Fermi-Bose Similarity
Minoru Omote,
Yoshio Ohnuki* and
Susumu Kamefuchi**
Institute of Physics, University of Tsukuba, Ibaraki 300-31
*Department of Physics, Nagoya University, Nagoya 464
**Department of Physics, Tokyo University of Education, Tokyo 112
(Received June 26, 1976)
Abstract:
The usual theory of the Lie algebras and the Lie groups is shown to be formally extended to the cases in which the group parameters commute and/or anticommute in the most general manner. It is then proved that the parafermi and parabose algebras for f degrees of freedom correspond to the Lie algebras of SO(2f+1) and of a graded version of Sp(2f, R), respectively. Further the trilinear and bilinear commutation relations for a general system comprising parafermi and parabose fields are shown to coincide with the Lie commutation relations of a certain group in the above-mentioned sense. Throughout our argumentation parafermi and parabose fields can formally be treated in ananalogous manner. It is thus concluded that the fermi-bose similarity that is known to hold in the ordinary field theory persists also in parafield theory.
URL :
http://ptp.ipap.jp/link?PTP/56/1948/
DOI : 10.1143/PTP.56.1948
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 67 No. 1 (1982) pp. 321-332
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Progress of Theoretical Physics Vol. 86 No. 6 (1991) pp. 1141-1148
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Partition Functions for Multilevel Parabosonic Systems
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Progress of Theoretical Physics Vol. 88 No. 1 (1992) pp. 149-153
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Thermodynamical Properties of High Order Parabosons
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Mitsuru Hama, Makoto Sawamura and Haruo Suzuki
