Quantization of the Myers-Pospelov model: The photon sector interacting with standard fermions as a perturbation of QED

Abstract

We study the quantization of the electromagnetic sector of the Myers-Pospelov model coupled to standard fermions. Our main objective, based upon experimental and observational evidence, is to construct an effective theory which is a genuine perturbation of QED, such that setting zero the Lorentz invariance violation parameters will reproduce it. To this end we provide a physically motivated prescription, based on the effective character of the model, regarding the way in which the model should be constructed and how the QED limit should be approached. This amounts to the introduction of an additional coarse-graining physical energy scale M , under which we can trust the effective field theory formulation. The prescription is successfully tested in the calculation of the Lorentz invariance violating contributions arising from the electron self-energy. Such radiative corrections turn out to be properly scaled by very small factors for any reasonable values of the parameters and no fine-tuning problems are found. Microcausality violations are highly suppressed and occur only in a space-like region extremely close to the light-cone. The stability of the model is guaranteed by restricting to concordant frames satisfying 1 − |vmax| > 6.5 × 10 −11 .

Einstein-Hilbert graviton modes modified by the Lorentz-violating bumblebee field

“…This theoretical framework has inspired a large number of investigations in the last several years, encompassing fermion systems [12][13][14][15][16][17][18][19][20], CPT-probing experiments [21][22][23][24][25][26][27], the electromagnetic CPT-and Lorentzodd term [28]- [41], the CPT-even and Lorentz-odd gauge sector and its interactions with fermions [42][43][44][45][46][47][48][49][50][51], [52][53][54][55][56][57]. Recent investigations involving higher dimensional operators [58][59][60], its possible connections with LV theories [61][62][63][64][65][66], and nonminimal couplings [67][68][69][70]…”

Lifshitz scaling to Lorentz-violating high derivative operator and gamma-ray bursts

“…(13) and (14) just recover the time-like background propagator connected to electromagnetic Myers-Pospelov Lagrangian in the Coulomb gauge [16]. The unitarity of the theory has been studied from the implementation of a physical cut-off both for the electron-positron scattering [17] and tree level [18].…”

Microcausality and quantization of the fermionic Myers–Pospelov model

“…The breakdown of Lorentz symmetry takes place in the scalar, fermion and gauge sectors and is characterized by an external timelike four-vector n µ defining a preferred reference frame. Experimental bounds for this model have been studied in several phenomena, such ⋆ a e-mail: justinux75@gmail.com b e-mail: creyes@ubiobio.cl as synchrotron radiation [5], gamma ray bursts [6], neutrino physics [7], radiative corrections [8,9], generic backgrounds [10,11], and others [12]. Typically, these phenomenological studies assume n to lie purely in the temporal direction [13].…”