Lorentz-preserving fields in Lorentz-violating theories

Abstract

Abstract. -We identify a fairly general class of field configurations (of spins 0, 1 2 and 1) which preserve Lorentz invariance in effective field theories of Lorentz violation characterized by a constant timelike vector. These fields concomitantly satisfy the equations of motion yielding cubic dispersion relations similar to those found earlier. They appear to have prospective applications in inflationary scenarios.Introduction. -Invariance under Lorentz transformation is known till date to be a global symmetry of the standard theory of elementary particles when gravitation is ignored. However, questions have been raised regarding the validity of this symmetry at small length scales owing to probable quantum gravity effects . The natural mass scale of quantum gravity is the Planck mass M P l . Departures, suppressed by the Planck mass, from the standard special relativistic dispersion relation of free particles of mass m at large energies have been accepted as a signature of Lorentz invariance violation and has been the principal objet de l'attention of experimental and theoretical probes of Lorentz violation. These hypothesised ad hoc corrections due to Lorentz non-invariance must have their origin in new terms in the action of the system. Myers and Pospelov [38] have studied this issue within the framework of effective field theory involving fields of spins 0, 1/2 and 1, by incorporating into the action dimension five operators containing a constant timelike 4-vector n which ostensibly breaks Lorentz invariance. Choosing a Lorentz frame where n µ = (1, 0), corrections of O(p 3 ) to the dispersion relation of each of the three fields have been obtained in [38] in the limit of relatively high energies E (M P l >> E >> m).

Perturbative generation of the higher-derivative Lorentz-breaking terms

“…One of the most interesting properties clearly calling attention to this term is the fact that it generates the rotation of the polarization plane of light. The problem of causality and stability with regard to these higher-derivative terms have been discussed in [15], the possible extension of the standard model by the three-derivative gauge terms, whose example is this term, has been discussed in [16], special properties of the classical solutions in theories with such terms have been discussed in [17], and a first example of the perturbative generation based on the use of the constant third-rank tensor has been proposed in [18].…”

A discussion on Lorentz preserving scalar fields in Lorentz violating theory

“…They may provide natural seeds for the growth of inhomogeneities in the early Universe [11]. An additional advantage is that these fields allow the use of standard Lorentz invariant formalism even in situations where Lorentz symmetry is violated.…”

“…We further investigate in the same section, the dispersion relation that these special field configurations satisfy. This work is based on our more extensive study [11] One must also have noticed that the additional term S V S in (1) contains third order derivatives of the field. Higher derivative Lagrangians are not new to physics [12].…”

Realisation of a Lorentz algebra in Lorentz violating theory

“…This new term contains a Planck suppressed dimension five operator with a constant background vector n that essentially assigns a preferred direction to spacetime. However, in [15], the authors demonstrate that there exist quite general field configurations which can restore Lorentz symmetry in the limit of infinitesimal transformations in modified action of [10]. These Lorentz preserving fields, as they have been named in [15], locally conserve the Nöther current for Lorentz transformations.…”

“…However, in [15], the authors demonstrate that there exist quite general field configurations which can restore Lorentz symmetry in the limit of infinitesimal transformations in modified action of [10]. These Lorentz preserving fields, as they have been named in [15], locally conserve the Nöther current for Lorentz transformations. Notice though that the Lorentz violation that had been woven into the Myers Pospelov theory is not lost.…”