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A proposal for a first class conversion formalism based on the symmetries of the Wess-Zumin.pdf

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A proposal for a first class conversion formalism based on the symmetries of the Wess-Zumin

a r X i v : h e p - t h / 0 1 1 2 1 5 9 v 2 4 D e c 2 0 0 2 Gauging by symmetries J. Ananias Neto?, C. Neves? and W. Oliveira? Departamento de F??sica, ICE, Universidade Federal de Juiz de Fora, 36036-330, Juiz de Fora, MG, Brazil Abstract We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamil- tonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this for- malism to important physical models: the reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the chiral bosons field theory. In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way. ?jorge@fisica.ufjf.br ?cneves@fisica.ufjf.br ?wilson@fisica.ufjf.br 1 J. Ananias Neto, C. Neves and W. Oliveira, ‘Gauging by symmetries’ 2 I. INTRODUCTION It is well known that through symmetries, important properties present on physical systems might be investigated in a more general way. In view of this, many works [1,2,3] have embedded second class systems into first class ones by enlarging the phase-space with the introduction of Wess-Zumino (WZ) variables. At the same time, an alternative gauge- invariant approach [4,5] has been proposed, which considers part of the total second class constraints as gauge fixing terms, while the remaining ones form a subset that satisfies a first class algebra. This formalism has an elegant property that does