Based on models of confinement of quarks, we analyse a relativistic scalar particle subject to a scalar potential proportional to the inverse of the radial distance and under the effects of the violation of the Lorentz symmetry. We show that the effects of the Lorentz symmetry breaking can induced a harmonic-type potential. Then, we solve the Klein-Gordon equation analytically and discuss the influence of the background of the violation of the Lorentz symmetry on the relativistic energy levels.
I will review results obtained recently within the Hamilton approach to QCD in Coulomb gauge. The focus will be on finite-temperature Yang--Mills theory and chiral symmetry breaking in QCD.
We calculate higher-order quantum contributions in different Lorentz-violating parameters to the gauge sector of the extended QED. As a result of this one-loop calculation, some terms which do not produce first-order corrections, contribute with nontrivial gauge-invariant second-order quantum inductions.
Anisotropy in the speed of light that has been constrained by Michelson-Morley-type experiments also generates anisotropy in the Coulomb interactions. This anisotropy can manifest itself as an energy anisotropy in nuclear and atomic experiments. Here the experimental limits on Lorentz violation in 21Ne are used to improve the limits on the Lorentz symmetry in the photon sector, namely the anisotropy of the speed of light and the Coulomb interactions, by 7 orders of magnitude in comparison with previous experiments: the speed of light is isotropic to a part in E-28.
We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear electrodynamics. The model is stable in the small Lorentz invariance violation approximation. The speed of light is independent of the frequency and one of the propagating modes is highly anisotropic. The bound (Delta c)/c < 10^{-32} is obtained for such anisotropy measured in perpendicular directions.
We consider an extended QED with the addition of a dimension-five Lorentz-breaking coupling between spinor and gauge fields, involving a pseudo-tensor $κ^{μνλρ}$. The specific form of the Lorentz violating coupling considered by us have been suggested in other works, and some of its consequences at the classical level were already studied. Here, we investigate the consequences of this specific form of Lorentz violation at the quantum level, evaluating the one loop corrections to the gauge field two-point function, both at zero and at finite temperature. We relate the terms that are generated b…
The new results by OPERA collaboration claim the discovery of superluminal neutrinos. Superluminal particles have to break Lorentzian symmetry or causality principle. The method discussed gives us the possibility to reintroduce Lorentzian symmetry without breaking of causality.
The toy fermion model coupled with Lagrange multiplier constraint field is proposed. The possibility of superluminal neutrino propagation as result of dynamical Lorentz symmetry breaking is studied.
Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type of wave functionals and includes the coupling of the quarks to the transversal spatial gluons. Using the lattice gluon propagator as input it is shown that the low energy chiral properties of the quarks, like the quark condensate and the constituent quark mass, are substantially increased by the coupling of the quarks to the spatial gluons. Our results compar…
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l=j-{1/2}, for any j.
In this work, we investigate the dynamical breakdown of Lorentz symmetry in 4 dimensions by the condensation of a fermionic field described by a Dirac Lagrangian with a four-fermion interaction. Using the Keldysh formalism we show that the Lorentz symmetry breaking modifies the Dyson-Schwinger equations of the fermionic propagator. We analyze the nonperturbative solutions for the Dyson-Schwinger equations using the combination of the rainbow and quenched approximations and show that, in equilibrium, the Lorentz symmetry breakdown can occur in the strong coupling regime and new features arise f…
We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving non-zero fermion number density to the vacuum (and therefore dynamically generating a chemical potential term). This mecanism yields a finite vacuum expectation value $<\barψγ^μψ>$ which we consider in the context of proposed models that require such a breaking of Lorentz invariance in order to yield composite degrees of freedom that act approximately like gauge bosons. We also make general remarks about how the background source provided by $<\ba…
We study the generation of aether-like Lorentz-breaking actions in three, four and five dimensions via an appropriate Lorentz-breaking coupling of electromagnetic and spinor fields. Special attention is given to the four-dimensional case where we discuss the issue of ambiguities.
The lagrangian-based Standard-Model Extension framework offers a broad description of possible gravitational effects from local Lorentz violation. In this talk, I review the status of the theoretical and phenomenological work in this area. The extension of previous results in linearized gravity to the nonlinear regime is discussed.
Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking.
In this paper we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a 'birefringence' effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wav…
Gravitational theories with Lorentz violation must account for a number of possible features in order to be consistent theoretically and phenomenologically. A brief summary of these features is given here. They include evasion of a no-go theorem, connections between spontaneous Lorentz breaking and diffeomorphism breaking, the appearance of massless Nambu-Goldstone modes and massive Higgs modes, and the possibility of a Higgs mechanism in gravity.
We study the effect of spontaneous breaking of Lorentz invariance on black hole thermodynamics. We consider a scenario where Lorentz symmetry breaking manifests itself by the difference of maximal velocities attainable by particles of different species in a preferred reference frame. The Lorentz breaking sector is represented by the ghost condensate. We find that the notions of black hole entropy and temperature loose their universal meaning. In particular, the standard derivation of the Hawking radiation yields that a black hole does emit thermal radiation in any given particle species, but w…
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions.
The relativistic three dimensional (3D) Lippmann-Schwinger-type equations for the $ep$ scattering amplitude is derived based on unitarity condition in the usual quantum electrodynamic (QED). The $ep$ scattering potential $V_{e'N',eN}$ consists of the leading one off mass shell photon exchange part and the nonlocal multi-particle exchange potential. Unlike to the other field-theoretical equations, both protons in the unitarity condition and in $V_{e'N',eN}$ are on mass shell. Therefore in this approach are not required the multi-variable input photon-nucleon vertexes with the off mass shell nuc…
In the context of N=4 supergravity in four dimensions, we present an exact classical solution that leads to spacetime-dependent electromagnetic couplings and discuss the ensuing Lorentz-violating effects. We comment briefly on experimental bounds.
Many candidate fundamental theories contain scalar fields that can acquire spacetime-varying expectation values in a cosmological context. Such scalars typically obey Lorentz-violating effective dispersion relations. We illustrate this fact within a simple supergravity model that also exhibits the observed late-time cosmological acceleration and implies varying electromagnetic couplings.
The breakdown of spacetime symmetries has recently been identified as a promising candidate signal for underlying physics, possibly arising through quantum-gravitational effects. This talk gives an overview over various aspects of CPT- and Lorentz-violation research. Particular emphasis is given to the interplay between CPT, Lorentz, and translation symmetry, mechanisms for CPT and Lorentz breaking, and the construction of a low-energy quantum-field description of such effect. This quantum field framework, called the SME, is employed to determine possible phenomenological consequences of CPT a…
The Lorentz nature of confinement in a heavy-light quarkonium is investigated. It is demonstrated that an effective scalar interaction is generated selfconsistently as a result of chiral symmetry breaking, and this effective scalar interaction is responsible for the QCD string formation between the quark and the antiquark.
One possible ramification of unified theories of nature such as string theory that may underlie the conventional standard model is the possible spontaneous breakdown of Lorentz and CPT symmetry. In this talk, the formalism for inclusion of such effects into a low-energy effective field theory is presented. An extension of the standard model that includes Lorentz- and CPT-breaking terms is developed. The restriction of the standard model extension to the QED sector is then discussed.
Low-energy remnant fundamental symmetry violations may be present in nature at levels attainable in upcoming experiments. These effects may arise through spontaneous symmetry breaking in a more complete Lorentz covariant theory underlying the standard model. In this work the issue of parameterizing such violations in a consistent and complete manner is addressed. The approach is to use the mechanism of spontaneous symmetry breaking to generate all possible terms consistent with gauge invariance and power-counting renormalizability to construct an extension of the standard model that includes L…
After imposing the Gauss law constraint as an initial condition upon the Hilbert space of the Nambu model, in all its generic realizations, we recover QED in the corresponding non-linear gauge A_μA^μ=n^{2}M^{2}. Our result is non-perturbative in the parameter M for n^{2}\neq 0 and can be extended to the n^{2}=0 case. This shows that in the Nambu model, spontaneous Lorentz symmetry breaking dynamically generates gauge invariance, provided the Gauss law is imposed as an initial condition. In this way electrodynamics is recovered, with the photon being realized as the Nambu-Goldstone modes of the…
If one modifies the Dirac equation in momentum space to $[γ^μp_μ-m-Δm(θ(p_{0})-θ(-p_{0})) θ(p_μ^{2})]ψ(p)=0$, the symmetry of positive and negative energy eigenvalues is lifted by $m\pm Δm$ for a small $Δm$. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations $θ(\pm p_{0})θ(p_μ^{2})$ with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but non-local at a distance scale of the Planck length. The application of this Lo…
In the context of an atom endowed with nuclear electric dipole moment (EDM), we consider the effects on the Schiff moment of $CPT$-even Lorentz-violating (LV) terms that modify the Coulomb potential. First, we study the modifications on the Schiff moment when the nucleus interacts with the electronic cloud by means of a Coulomb potential altered only by the $P$-even LV components. Next, by supposing the existence of an additional intrinsic LV EDM generated by other LV sources, we assess the corrections to the Schiff moment when the interaction nucleus-electrons runs mediated by a Coulomb poten…
We analyze the unitarity of a modified QED with higher-order terms that violate Lorentz symmetry. We make an explicit calculation to verify unitarity at the one-loop level. As expected we find negative norm states that could in principle lead to a violation of unitarity. However, we show that these states become massive in Euclidean space and do not contribute to the discontinuity.
Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.
We investigate inertial frames in the absence of Lorentz invariance, reconsidering the usual group structure implied by the relativity principle. We abandon the relativity principle, discarding the group structure for the transformations between inertial frames, while requiring these transformations to be at least linear (to preserve homogeneity). In theories with a preferred frame (aether), the set of transformations between inertial frames forms a groupoid/pseudogroup instead of a group, a characteristic essential to evading the von Ignatowsky theorems. In order to understand the dynamics, w…
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…
Classical superstring vacua have zero vacuum energy and are supersymmetric and Lorentz-invariant. We argue that all these properties may be destroyed when quantum aspects of the interactions between particles and non-perturbative vacuum fluctuations are considered. A toy calculation of string/D-brane interactions using a world-sheet approach indicates that quantum recoil effects - reflecting the gravitational back-reaction on space-time foam due to the propagation of energetic particles - induce non-zero vacuum energy that is linked to supersymmetry breaking and breaks Lorentz invariance. This…
Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation …
We consider the gauge theory of Lorentz group coupled in a nonminimal way to fermions. We suggest the hypothesis that the given theory may exist in the phase with broken chiral symmetry and without confinement. The lattice discretization of the model is described. This unusual strongly coupled theory may appear to be the source of the dynamical electroweak symmetry breaking. Namely, in this theory all existing fermions interact with the SO(3,1) gauge field. In the absence of the other interactions the chiral condensate may appear and all fermionic excitations may acquire equal masses. Small co…
In this paper we study the breaking of chiral symmetry with non-confining power-like potentials. The region of allowed exponents is identified and, after the previous study of confining (positive exponent) potentials, we now specialize in shorter range non-confining potentials, with a negative exponent. These non-confining potentials are close to the Coulomb potential, and they are also relevant as corrections to the linear confinement, and as models for the quark potential at the deconfinement transition. The mass-gap equation is constructed and solved, and the quarks mass, the chiral angle a…
A number of different approaches to quantum gravity are at least partly phenomenologically characterized by their treatment of Lorentz symmetry, in particular whether the symmetry is exact or modified/broken at the smallest scales. For example, string theory generally preserves Lorentz symmetry while analog gravity and Lifshitz models break it at microscopic scales. In models with broken Lorentz symmetry there are a vast number of constraints on departures from Lorentz invariance that can be established with low energy experiments by employing the techniques of effective field theory in both t…
A quantum field model for Dirac-like tachyons respecting a frame-dependent interpretation rule, and thus inherently breaking Lorentz invariance, is defined. It is shown how the usual paradoxa ascribed to tachyons, instability and acausality, are resolved in this model, and it is argued elsewhere that Lorentz symmetry breaking is necessary to permit perturbative renormalizability and causality. Elimination of negative-normed states results in only left-handed particles and right-handed antiparticles, suitable for describing the neutrino. In this context the neutron beta decay spectrum is calcul…
Spontaneous breaking of Lorentz invariance may take place in string theories, possibly endowing the photon with a mass. This leads to the breaking of the conformal symmetry of the electromagnetic action allowing for the generation within inflationary scenarios of magnetic fields over $Mpc$ scales. We show that the generated fields are consistent with amplification by the galactic dynamo processes and can be as large as to explain the observed galactic magnetic fields through the collapse of protogalactic clouds.
Previous studies on high-energy gamma-ray burst neutrinos from IceCube suggest a neutrino speed variation at the Lorentz violation~(LV) scale of $\sim 6.4\times 10^{17}$~GeV, with opposite velocity variances between neutrinos and antineutrinos. Within a space-time foam model, inspired by string theory, we develop an approach to describe the suggested neutrino/antineutrino propagation properties with both Lorentz invariance and CPT symmetry breaking. A threshold analysis on the bremsstrahlung of electron-positron pair~($ν\rightarrowνee^{+}$) for the superluminal~(anti)neutrino is performed. We …
Spontanous symmetry breaking usually gives spin 0 Goldstone bosons for the case of internal symmetries and spin 1/2 fermions for the supersymmetry. The spontaneous breaking of higher dimensional Lorentz symmetry can give vector Goldstone boson in 4-dimension.
We address the question of the Lorentz nature of the effective interquark interaction in QCD which leads to the formation of the QCD string between colour charges. In particular, we start from a manifestly vectorial fundamental interaction mediated by gluons and demonstrate that, as soon as chiral symmetry is broken spontaneously, the effective interquark interaction acquires a selfconsistently generated scalar part which is eventually responsible for the formation of the QCD string. We demonstrate this explicitly for a heavy-light quarkonium, using the approach of the Schwinger-Dyson-type equ…
A popular framework for exploring Lorentz violation is the Standard Model Extension. This extension contains a large number of parameters that can be bounded in various experiments. Most studies, however, focus on the fermion or photon sector. Here, we consider Lorentz violation in the weak vector boson sector. The strongest bounds come from measurements of the asymmetry in Moller scattering. We study the bounds that can be obtained from future measurements of the parity violating asymmetry in deep inelastic electron-proton scattering at the EIC, the LHeC and the FCC-eh. For the FCC-eh, the bo…
A tiny Lorentz symmetry breaking can be mediated in Electrodynamics by means of the Chern-Simons (CS) interaction polarized along a constant CS vector. Its presence makes the vacuum optically active that has been recently estimated from astrophysical data. We examine two possibilities for the CS vector to be time-like or space-like, under the assumption that it originates from v.e.v. of some pseudoscalar matter. It is shown that: a) a time-like CS vector makes the vacuum unstable under pairs creation of tachyonic photon modes with the finite vacuum decay rate, i.e. it is unlikely realized at m…
We show that estimates of the Lorentz symmetry violation extracted from ultra-high energy cosmic rays beyond the GZK cut-off set bounds on the parameters of a Lorentz-violating extension of the Standard Model. Moreover, we argue that correlated measurements of the difference in the arrival time of gamma-ray photons and neutrinos emitted from Active Galactic Nuclei or Gamma-Ray Bursts may provide a signature for a possible violation of the Lorentz symmetry. We find that this time delay is energy independent, but that it has a dependence on the chirality of the particles involved.
Spontaneous breaking of Lorentz invariance compatible with observational limits may realistically take place in the context of string theories, possibly endowing the photon with a mass. In this process the conformal symmetry of the electromagnetic action is broken allowing for the possibility of generating large scale ($\sim Mpc$) magnetic fields within inflationary scenarios. We show that for reheating temperatures safe from the point of view of the gravitino and moduli problem, $T_{RH} \laq 10^{9} GeV$ for $m_{3/2} \approx 1 TeV$, the strength of the generated seed fields is, in our mechanis…
In the context of Standard Model Extensions (SMEs), we analyse four general classes of Super Symmetry (SuSy) and Lorentz Symmetry (LoSy) breaking, leading to {observable} imprints at our energy scales. The photon dispersion relations show a non-Maxwellian behaviour for the CPT (Charge-Parity-Time reversal symmetry) odd and even sectors. The group velocities exhibit also a directional dependence with respect to the breaking background vector (odd CPT) or tensor (even CPT). In the former sector, the group velocity may decay following an inverse squared frequency behaviour. Thus, we extract a mas…
