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Title:
Non-Linear Realizations of ’Distortion’ Group
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Phenomenological Lagrangians ; Symmetry breaking ; non-linear realizations of Lie group ; Maurer-Cartan’s equations ; Conserved currents
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Abstract:
In the framework of the method of phenomenological Lagrangians, we address the non-linear realizations of the Lie group G concerning the ’distortion’ of 12-dimensional space. Treating the ’distortion’ group G and its stationary subgroup H = SO(3), respectively, as the dynamical group and its algebraic subgroup, we identify the parameters of the quotient space G/H of adjacent classes by the subgroup H with the Goldstone fields of spontaneous breaking of ’distortion’ symmetry. We study the geometrical structure of the space of parameters in terms of Cartan forms introduced through the appropriate Maurer- Cartan’s structure equations. This allows us to infer the group invariants and calculate the conserved currents as its inevitable corollaries.