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Prog. Theor. Phys. Vol. 61 No. 5 (1979) pp. 1499-1514

Quanta of Non-Abelian Gauge Field Can Be Transversal?

Takao Okabayashi

Department of Physics, University of Tokyo, Tokyo 113

(Received December 15, 1978)

Abstract:

Transverse non-abelian gauge field is usually described by canonical conjugate variables \hatB and G. It is easy to express G in terms of gauge field \hatB, its time derivative ∂₀\hatB, and source fields. Then, in quantum theory, we have three methods to calculate ∂₀²\hatB, and each of them gives a different expression to double commutator terms in wave equation of gauge field. The discrepancy is purely quantum-theoretical. Its origin is in the facts that covariant derivative of gauge field depends on ∂₀\hatB in a non-trivial way, and that there are two operators to project ∂₀\hatB out of the covariant derivative. In short, there is yet no satisfactory quantum theory of transverse non-abelian gauge field, although we have consistent classical lagrangian formalism for the field.

URL : http://ptp.ipap.jp/link?PTP/61/1499/
DOI : 10.1143/PTP.61.1499

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 62 No. 1 (1979) pp. 201-213 :

   T^*-Product Convention for Quasi-Linear Systems and for Transverse Non-Abelian Gauge Fields

   Takao Okabayashi

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