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Underlying gauge symmetries of second-class constraints systems | | M.I. Krivoruchenko
; Amand Faessler
; A.A. Raduta
; C. Fuchs
; | | Date: |
21 Jun 2005 | | Subject: | hep-th | | Affiliation: | Moscow, ITEP & Tubingen U.), Amand Faessler (Tubingen U.), A.A. Raduta (Tubingen U. & Bucharest U. & Bucharest, IFIN-HH), C. Fuchs (Tubingen U. | | Abstract: | Gauge-invariant systems in the 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 the underlying dilatation symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in an extended configuration space. The systems under second-class holonomic constraints have gauge-invariant counterparts within the 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 surfaces into the unconstrained phase space. | | Source: | arXiv, hep-th/0506178 | | Services: | Forum | Review | PDF | Favorites | |
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