Prog. Theor. Phys. Vol. 81 No. 2 (1989) pp. 523-540

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A Spinor Approach to Poincaré Gauge Theory

— In a Case of Massless Lorenz Gauge Field —

Shin-ichi Nakariki

Department of Applied Physics, Okayama University of Science, Okayama 700

(Received February 15, 1988)

Abstract:

We formulate a spinor formalism for Poincaré gauge theory in vacuum in linear approximation with the condition α+ (2/3)a = β-(2/3)a = γ+ (3/2)a = 0. The spinor formalism introduces the notion of a null tetrad in a remarkably natural way, and will be useful to study massless fields. The existence of massless modes in a Lorenz gauge field was investigated in the above mentioned condition by two groups. One of them found two massless modes propagating with positive energy. On the contrary, the other group claimed the nonexistence of the massless modes. In order to dissolve this confusing situation we apply our formalism to the investigation of a “null field” in the Lorenz gauge field. We find two such modes with spin-parity 1⁺ and 1^-, which cannot coexist. This is consistent with the result given by one of the above groups. However, our conditions for the parameters are more stringent than theirs. The difference seems to come from our elimination of unphysical fields which do not appear in the energy density. In fact, when they are not eliminated, we have the same conditions as theirs.

URL : http://ptp.ipap.jp/link?PTP/81/523/
DOI : 10.1143/PTP.81.523

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Citing Article(s) :

Progress of Theoretical Physics Vol. 88 No. 2 (1992) pp. 291-305 :
Asymptotic Anti-De Sitter Conditions for Poincaré Gauge Theory

Roh-Suan Tung, Chun-Hsu Chang, De-Ching Chern and James M. Nester
Progress of Theoretical Physics Vol. 107 No. 1 (2002) pp. 191-210 :
Massless Modes of Lorentz Gauge Fields in Poincaré Gauge Theory of Gravity

Kazumi Fukuma