G Helesfai 2008 Class. Quantum Grav. 25 235010 doi:10.1088/0264-9381/25/23/235010
G Helesfai
Show affiliationsIn this paper we investigate the question of how spontaneous symmetry breaking works in the framework of loop quantum gravity and compare it to the results obtained in the case of the Proca field, where we were able to quantize the theory in loop quantum gravity without introducing a Higgs field. We obtained that the Hamiltonian of the two systems is very similar, the only difference is an extra scalar field in the case of spontaneous symmetry breaking. This field can be identified as the field that carries the mass of the vector field. In the quantum regime this becomes a well-defined operator, which turns out to be a self-adjoint operator with continuous spectrum. To calculate the spectrum we used a new representation in the case of scalar fields, which in addition enabled us to rewrite the constraint equations to a finite system of linear partial differential equations. This made it possible to solve part of the constraints explicitly.
04.60.Pp Loop quantum gravity, quantum geometry, spin foams
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
Issue 23 (7 December 2008)
Received 20 June 2008, in final form 8 September 2008
Published 17 November 2008
G Helesfai 2008 Class. Quantum Grav. 25 235010
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