Symmetries in Fundamental Physics

Abstract. We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields. The matter fields are represented by a mesoscopic polarization field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalized Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

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“…We can rephrase the problem we discussed above also by referring to the ideas developed in [17]. See also [18], pp. 356-360.…”

Section: Covariance Of the Theory Under The Poincaré Group And Causalitymentioning

confidence: 99%

Exact quantisation of the relativistic Hopfield model

et al. 2016

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“…We will summarize Dirac's procedure for constrained Hamiltonian systems, [31][32][33] for later use in a couple of toy models. Let be a Lagrangian L = L(q k ,q k ) such that the equations defining the canonical momenta p k = ∂L/∂q k cannot be unambiguously solved for all the velocities.…”

Section: A Counting Degrees Of Freedom In Constrained Hamiltonian Symentioning

confidence: 99%

Pseudoinvariance and the extra degree of freedom inf(T)gravity

Ferraro

Guzmán

2020

Phys. Rev. D

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Non-linear generalizations of teleparallel gravity entail the modification of a Lagrangian that is pseudo-invariant under local Lorentz transformations of the tetrad field. This procedure consequently leads to the loss of the local pseudo-invariance and the appearance of additional degrees of freedom (d.o.f.). The constraint structure of f (T ) gravity suggests the existence of one extra d.o.f. when compared with GR, which should describe some aspect of the orientation of the tetrad. The purpose of this article is to better understand the nature of this extra d.o.f. by means of a toy model that mimics essential features of f (T ) gravity. We find that the non-linear modification of a Lagrangian L possessing a local rotational pseudo-invariance produces two types of solution. In one case the original gauge invariant variables -the analogue of the metric in teleparallelism-evolve like when governed by the (non-deformed) Lagrangian L; these solutions are characterized by a (selectable) constant value of its Lagrangian, which is the manifestation of the extra d.o.f. In the other case, the solutions do contain new dynamics for the original gauge invariant variables, but the extra d.o.f. does not materialize because the Lagrangian remains invariant on-shell. Coming back to f (T ) gravity, the first case includes solutions where the torsion scalar T is a constant, to be chosen at the initial conditions (extra d.o.f.), and no new dynamics for the metric is expected. The latter case covers those solutions displaying a genuine modified gravity; T is not a constant, but it is (on-shell) invariant under Lorentz transformations depending only on time. Both kinds of f (T ) solutions are exemplified in a flat FLRW universe. Finally, we present a toy model for a higher order Lagrangian with rotational invariance (as analogous to f (R) gravity) and derive its constraint structure and number of d.o.f..CONTENTS

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“…The original view, which retains manifest equivalence to the Lagrangian and which disappeared as the 1950s wore on and started reappearing around 1980, is that gauge transformations are generated by a tuned sum of first-class constraints (primary, secondary, etc. ), the "gauge generator" G [2,11,29,40,45,48]. For Maxwell's electromagnetism the gauge generator is…”

Section: First-class Constraints and Gauge?mentioning

confidence: 99%