By John M Charap

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Tchrakian (1994), 'Skyrme like models in gauge theory', in Constraint Theory and Quantization Methods, F. Colomo, L. Lusanna and G. Marmo (eds), World Scientific. H. Tchrakian (1985), Phys. Lett, B150 360. Downloaded from University Publishing Online. 250 on Tue Jan 24 04:02:39 GMT 2012. 005 Exponentially localised instantons in a hierarchy of Higgs models 31 [3] J. H. Tchrakian (1994), J. , A26 L1053. N. H. Tchrakian (1986), J. Math. M. H. Tchrakian (1986), Phys. H. Tchrakian (1988), ibid, D38 3827.

Our reduced dynamical system (12) has five degrees of freedom, parametrized by the coordinates X , \j> and the conjugate momenta P = dL/dX, HT = dL/dip. The invariance of the original action under diffeomorphisms implies the invariance of (12) under SO(2,1) transformations, which leads to the conservation of the angular momentum vector J = L + S, (15) sum of 'orbital' and 'spin' contributions given by L = XAP, S = \xfE^. (16) It follows that, as implied by the notation, the components gab of the metric tensor transform vectorially under the action of S0(2,l), while the gauge potentials transform spinorially.

The invariance of the original action under diffeomorphisms implies the invariance of (12) under SO(2,1) transformations, which leads to the conservation of the angular momentum vector J = L + S, (15) sum of 'orbital' and 'spin' contributions given by L = XAP, S = \xfE^. (16) It follows that, as implied by the notation, the components gab of the metric tensor transform vectorially under the action of S0(2,l), while the gauge potentials transform spinorially. In the case \x — 0, the coordinates \j)a are cyclic, so that the two corresponding degrees of freedom may be eliminated altogether [7].