Quick Search:
Prog. Theor. Phys. Vol. 77 No. 6 (1987) pp. 1484-1508
The Second Rank Tensor Field, a Systematic Study
— Classification of the Second Rank Tensor Field Theories
—
Anton Z. Capri,
Masanori Kobayashi and
Yoshio Ohnuki*
Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1
*Department of Physics, Nagoya University, Nagoya 464
(Received October 27, 1986)
Abstract:
By assuming the existence of a Klein-Gordon divisor, we obtain nine classes of subsidiary conditions, in terms of which we classify the theories for massive tensor fields of rank two. We rediscover the higher-spin field theories for pure spin-one and spin-zero. All the theories corresponding to various mixed spin contents are reducible. Among these we succeed in describing the pure spin-one content in terms of the symmetric tensor field of rank two.
URL :
http://ptp.ipap.jp/link?PTP/77/1484/
DOI : 10.1143/PTP.77.1484
References:
- M. Fierz and W. Pauli, Proc. R. Soc. London A173 (1939), 211.
- Y. Takahashi and H. Umezawa, Prog. Theor. Phys. 9 (1953), 14, [PTP]50;
Nucl. Phys. 51 (1964), 193[CrossRef]. See also H. Umezawa, Quantum Field Theory (North-Holland, Amsterdam, 1956); Y. Takahashi, An Introduction to Field Quantization (Pergamon, New York, 1969).
- In the most general quadratic second-order langrangian for massive particles with integer spin-J, the number of parameters contained in the langrangian is (J+2)(2J)!(2JJ!). For instance, the numbers of parameters contained in the langrangian and the Klein-Gordon divisor are 75 and 150 for J=3 and 630 and 1365 for J=4, respectively.
-
H. Umezawa and A. Visconti, Nucl. Phys. 1 (1956), 348[Elsevier].
-
J. Schwinger, Phys. Rev. 82 (1951), 914[APS];
ibid. 91 (1953), 731[APS].
- A. S. Wightman, private communication.
- R. J. Rivers, Nuovo Cim. 34 (1964), 386.
-
S. C. Bhargava and H. Watanabe, Nucl. Phys. 87 (1953), 273[CrossRef].
-
Y. Takahashi and R. Palmer, Phys. Rev. D1 (1970), 2974[APS].
-
A. J. MacFarlane and W. Tait, Commun. Math. Phys. 24 (1972), 211[CrossRef].
- Z. Tokuoka, private communication. See also A. Z. Capri and M.Kobayashi, Prog. Theor. Phys. 74 (1985), 368[PTP]; Massive totally antisymmetric tensor fields, a systematic study, to appear in Nuovo Cim. (1987).
- A. Z. Capri and M. Kobayashi, J. of Phys. A18 (1985), 2561.
