XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

Diego Julio Cirilo-Lombardo

Dynamical symmetries, coherent states and noncommutative structures: geometrical quantization analysis

The relation between fundamental spacetime structures and dynamical symmetries are treated
from the geometrical and topological viewpoint. To this end analyze, taking into account the
concept of categories and quasi hamiltonian structures, a recent research [ Int.J.Geom.Meth.Mod.Phys. 15 (2017) no.01, 1850005]where one linear
and one quadratic in curvature models were constructed and where a dynamical breaking of the
SO(4, 2) group symmetry arises. We explain there how and why coherent states of the KlauderPerelomov
type are defined for both cases taking into account the coset geometry and some hints
on the possibility to extend they to the categorical (functorial) status are given. The new spontaneous
compactification mechanism that was defined in the subspace invariant under the stability
subgroup. The physical implications of the symmetry rupture as the introduction of a noncommutative
structure in the context of non-linear realizations and direct gauging are analyzed and
briefly discussed.

Event sponsored by:
of Bialystok
University of Bialystok

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