Lorentz Breaking Effective Field Theory and Observational Tests

Abstract

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.

Velocity-dependent deformations of the energy spectrum of a quantum cavity from Lorentz symmetry violations

“…Therefore, {â n ,â † n } will only satisfy the algebra of creation and annihilation operators if {ψ n , ψ * n } satisfies (52). From the formula (30), we obtain the following expression for the Hamiltonian operator 4 We comment that part of the reason for introducing a finite cutoff in our mode expansion is that the issue of the invertibility is considerably more complicated in the infinite dimensional case. If we take the matrix dimension 2N to be infinite a priori, it is possible that only one of the left-or right-inverses of S might exist.…”

“…This has led many authors to speculate that Lorentz symmetry is an emergent phenomena that only holds approximately at large scales, and it is therefore possible for very high energy or smallscale experiments to detect Lorentz invariance violations (see refs. [1][2][3][4][5][6] for reviews). Specific models exhibiting Lorentz symmetry violation have been obtained in the context of string theory [7][8][9][10][11][12][13][14], loop quantum gravity [15][16][17][18], and non-commutative geometry [19][20][21][22][23][24][25][26][27] (for other examples see [1] and references therein).…”

“…While astrophysical observations represent the best means we have to constrain higher dimensional Lorentzviolating operators, it is obviously useful to have independent and reproducible laboratory-based techniques for probing these effects. These include clock-comparison experiments [57][58][59][60], Penning traps [59,61,62] and doppler shift experiments (for a more comprehensive discussion, see [1][2][3][4][5][6]).…”

Einstein-aether theory with a Maxwell field: General formalism

“…According to the principles of effective field theories (see, e.g., [27][28][29][30][31]) one can establish some interrelations between the terms in the action functional and differential operators of the first, second, and higher orders. In the Appendix A we give the complete set of terms that could be included in the action if one selects terms with derivatives up to the fourth order.…”

Axionic extension of the Einstein-aether theory

“…In this paper we establish the version of the Einsteinaether-axion theory, which can be classified as the theory of the second order with respect to the Effective Field theory. (see, e.g., [42][43][44][45][46] for details, terminology and historical remarks). Mathematically, we extend the Lagrangian by inserting all possible cross-terms, which, on the one hand, contain the vector field U i , and the tensor ∇ i U k , the covariant derivative of the unit vector field, and, on the other hand, include pseudoscalar (axion) field φ and its gradient four-vector ∇ i φ.…”