Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-06-21
Int.J.Mod.Phys. A22 (2007) 787-834
Physics
High Energy Physics
High Energy Physics - Theory
23 pages REVTeX, new references added
Scientific paper
Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an $n-1$-dimensional sphere $S^{n-1}$ as an example of a mechanical second-class constraints system and the O(n) non-linear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.
Faessler Amand
Fuchs Ch.
Krivoruchenko M. I.
Raduta A. A.
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