Conditions for the emergence of gauge bosons from spontaneous Lorentz symmetry breaking

Abstract

The emergence of gauge particles (e.g., photons and gravitons) as Goldstone bosons arising from spontaneous symmetry breaking is an interesting hypothesis which would provide a dynamical setting for the gauge principle. We investigate this proposal in the framework of a general SO(N ) non-Abelian Nambu model (NANM), effectively providing spontaneous Lorentz symmetry breaking in terms of the corresponding Goldstone bosons. Using a nonperturbative Hamiltonian analysis, we prove that the SO(N ) Yang-Mills theory is equivalent to the corresponding NANM, after both current conservation and the Gauss laws are imposed as initial conditions for the latter. This equivalence is independent of any gauge fixing in the YM theory. A substantial conceptual and practical improvement in the analysis arises by choosing a particular parametrization that solves the nonlinear constraint defining the NANM. This choice allows us to show that the relation between the NANM canonical variables and the corresponding ones of the YM theory, A a i and E bj , is given by a canonical transformation. In terms of the latter variables, the NANM Hamiltonian has the same form as the YM Hamiltonian, except that the Gauss laws do not arise as first-class constraints. The dynamics of the NANM further guarantees that it is sufficient to impose them only as initial conditions, in order to recover the full equivalence. It is interesting to observe that this particular parametrization exhibits the NANM as a regular theory, thus providing a substantial simplification in the calculations.

Testing Lorentz and CPT invariance with ultracold neutrons

“…One candidate set of Planck scale signals is relativity violations, which are associated with the breaking of Lorentz and CPT symmetries, hence the considerable amount of attention it has gained in the past two decades. Some modern approaches to QTG, such as noncommutative field theories [1], quantum gravity [2], string theory [3], brane-worlds scenarios [4], condensed matter analogues of "emergent gravity" [5], Hořava-Lifshitz gravity [6][7][8], gauge emergent bosons [9], and other Lorentzviolating scenarios [10][11][12], are examples that lead to setups in which Lorentz invariance is no longer an exact symmetry.…”

Local effects of the quantum vacuum in Lorentz-violating electrodynamics

“…Interest in Lorentz violation [1][2][3][4][5][6] has grown rapidly in the last decades since many candidate theories of quantum gravity [7,8], such as string theory [9] and loop quantum gravity [10], possess scenarios involving deviations from Lorentz symmetry. Nowadays, investigations concerning Lorentz violation are mostly conducted under the framework of the standard model extension (SME), initiated by Kostelecký and Colladay [11,12].…”

Casimir effect between ponderable media as modeled by the standard model extension

“…The precise problem we tackle in this paper is the Casimir effect between two Lorentz-violating ponderable media as modeled by the constitutive relations (10), in which case the boundaries play a prominent role. To perform the analysis, we require to study the effects of the vacuum-medium interface, which we denote as Σ, in the propagation of the electromagnetic fields.…”

“…The question that naturally arises is whether the Lorentz invariance holds exactly or to what extent it holds. Motivated by the unknown underlying theory of quantum gravity [2,3], the possible Lorentz symmetry violation effects have been investigated from various theories, for example, noncommutative field theories [4], loop quantum gravity [5], string theory [6], brane-worlds scenarios [7], condensed matter analogues of "emergent gravity" [8], among others Lorentz violating scenarios [9,10].…”