Prog. Theor. Phys. Vol. 73 No. 4 (1985) pp. 1025-1042
Relation between Generators of Gauge Transformations and Subsidiary Conditions on State Vectors
— Point Mechanical Systems with Arbitrary Numbers of Constraints
Department of Physics, Osaka City University, Osaka 558
*Research Institute for Atomic Energy, Osaka City University, Osaka 558
**Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725
(Received October 22, 1984)
A general formulation of quantization of gauge theories is studied by imposing a subsidiary condition on state vectors in the Hilbert space in order to remove unphysical gauge components. The subsidiary condition is made of the generator of gauge transformations which is a linear combination of the first class constraints. The procedure is applied to a typical model of point mechanics which has characteristic features of Abelian gauge theories with series of arbitrary numbers of secondary constraints. It is sufficient to employ a single subsidiary condition for each gauge degree of freedom in order to remove all unphysical gauge components originated from the series of secondary constraints. Half of the gauge components turn out to be unphysical states and the other half to be physical but zero norm states. Indefinite metric appears even in point mechanics.
DOI : 10.1143/PTP.73.1025
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Citing Article(s) :
Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 283-301
Generator of Gauge Transformation in Phase Space and Velocity Phase Space
Reiji Sugano, Yoshihiko Saito and Toshiei Kimura