Narrow Results

This paper is devoted to introduce a gauge theory of the Lorentz group based on the ambiguity emerging in dealing with isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat spacetime and the role of the torsion field, within the generalization to curved spacetime, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.

This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to "Lorentz breaking" effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to lose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres, Bi et al., and Cowsik et al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these anomalous processes are forbidden if Lorentz symmetry is instead "deformed", preserving the relativity of inertial frames. These deformations add nonlinear terms to energy–momentum relations, conservation laws and Lorentz transformations in a way that is consistent with the relativity of inertial observers.

We study emergent Yang–Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang–Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.

One kind of spontaneous (2 + 1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is SO(2, 1) $\to$ SO(1, 1). Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu–Goldstone bosons is obtained.

In this paper, we discuss the ultraviolet sector of (3 + 1)-dimensional Lifshitz-type anisotropic higher derivative scalar, fermion and gauge field theories, with anisotropy exponent $z=3$ and with explicit breaking of Lorentz symmetry. By discarding from the action of all momentum-dependent vertex operators, which is essential to avoid phenomenologically unacceptable deformations of the light cone, we find that renormalizable scalar self-interaction and Yukawa-like couplings are, in general, asymptotically free. However, the requirement of cancelling momentum-dependent vertex operators is incompatible with gauge symmetry and, therefore, for this kind of theories, gauge symmetry as well as Lorentz symmetry are recovered only as emergent properties below some energy scale $M$, that must be constrained from experiments. The quantum corrections to the scalar mass and their impact on the hierarchy problem are also analyzed.

We consider some alternative scenarios for the fate of Poincaré/Lorentz symmetry at the Planck scale, and we discuss some opportunities to test these scenarios.

It is shown that by imposing the relativistic symmetries on the cutoff in field theories, one rules out all known nonperturbative regulators except the point splitting. The relativistic cutoff dynamics is nonlocal in time and thereby unstable, bringing the very existence of relativistic field theory into question. A stable, relativistic regulator is proposed for a scalar field theory model and its semiclassical stability is shown numerically.

The Abraham–Lorentz force is a finite remnant of the UV singular structure of the self-interaction of a point charge with its own field. The satisfactory description of such an interaction needs a relativistic regulator. This turns out to be a problematic point because the energy of regulated relativistic cutoff theories is unbounded from below. However, one can construct point-splitting regulators which keep the Abraham–Lorentz force stable. The classical language can be reconciled with QED by pointing out that the effective quantum theory for the electric charge supports a saddle point producing the classical radiation reaction forces.

The Lorentz transformation describes differential simultaneity, which reflects the offsetting of time with distance between reference frames. Differential simultaneity is essential for Lorentz invariance. Here, the current experimental support for differential simultaneity is assessed. Differential simultaneity can be mathematically removed from the Lorentz transformation to produce an alternate transformation that describes relativistic effects in the absence of differential simultaneity. Differential simultaneity is shown to be required for Lorentz symmetry. The alternate transformation is used as a contrast for the Lorentz transformation to assess whether relativistic experiments provide definitive evidence for differential simultaneity. If the alternate transformation is compatible with an experiment, then the experiment does not provide definitive evidence for differential simultaneity because it can be explained in the absence of differential simultaneity. Here, the alternate transformation is shown to be compatible with the broad array of current relativistic experiments. This implies that current experiments do not provide definitive evidence for differential simultaneity. Thus, an essential aspect of Lorentz symmetry currently lacks definitive experimental support.

Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: What is the fate of the Nambu–Goldstone (NG) modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.

We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA data on superluminal neutrinos. On one side we stress that some aspects of this result are puzzling even from the perspective of the wild quantum-gravity literature, where arguments in favor of the possibility of superluminal propagation have been presented, but not considering the possibility of such a sizeable effect for neutrinos of such low energies. We feel this must encourage particularly severe scrutiny of the OPERA result. On the other side, we notice that the OPERA result is reasonably consistent with μ-neutrino-speed data previously obtained at FERMILAB, reported in papers of 2007 and 1979. And it is intriguing that these FERMILAB79 and FERMILAB07 results, when combined with the new OPERA result, in principle provide a window on μ-neutrino speeds at different energies broad enough to compare alternative phenomenological models. We test the discriminating power of such an approach by using as illustrative examples the case of special-relativistic tachyons, the case of momentum-independent violations of the special-relativistic speed law, and the cases of linear and quadratic energy dependence of the speed of ultrarelativistic muon neutrinos. Even just using μ-neutrino data in the range from ~3 GeVs to ~200 GeVs the special-relativistic tachyon and the quadratic-dependence case are clearly disfavoured. The linear-dependence case gives a marginally consistent picture and the momentum-independent scenario fits robustly the data. We also comment on Supernova 1987a and its relevance for consideration of other neutrino species, also in relation with some scenarios that appeared in the large-extra-dimension literature.

In this paper, we first show that the definition of the universal horizons studied recently in the khronometric theory of gravity can be straightforwardly generalized to other theories that violate the Lorentz symmetry, by simply considering the khronon as a probe field and playing the same role as a Killing vector field. As an application, we study static charged (D + 1)-dimensional spacetimes in the framework of the healthy (nonprojectable) Horava–Lifshitz (HL) gravity in the infrared (IR) limit, and find various solutions. Some of them represent Lifshitz spacetimes with hyperscaling violations, and some have black hole structures. In the latter, universal horizons always exist inside the Killing horizons. The surface gravity on them can be either larger or smaller than the surface gravity on the Killing horizons, depending on the spacetimes considered. Although such black holes are found only in the IR, we argue that black holes with universal horizons also exist in the full theory of the HL gravity. A simple example is the Schwarzschild solution written in the Painleve–Gullstrand coordinates, which is also a solution of the full theory of the HL gravity and has a universal horizon located inside the Schwarzschild Killing horizon.

Universal horizons in Hořava–Lifshitz gravity and Einstein-æther theory are the equivalent of causal horizons in general relativity and appear to have many of the same properties, including a first law of horizon thermodynamics and thermal radiation. Since universal horizons are infrared (IR) solutions of a putative power counting renormalizable quantum gravitational theory, fully understanding their thermodynamics will shed light on the interplay between black hole thermodynamics and quantum gravity. In this paper, we provide a complete classification, including asymptotic charges, of all four-dimensional static and spherically symmetric universal horizon solutions with maximally symmetric asymptotics — the equivalents of the Schwarzschild, Schwarzschild–de Sitter or Schwarzschild–anti-de Sitter spacetimes. Additionally, we derive the associated first laws for the universal horizon solutions. Finally, we prove that independent of asymptotic boundary conditions, any spherically symmetric solution in Hořava–Lifshitz gravity with a universal horizon is also a solution of Einstein-æther theory, thereby broadening and complementing the known equivalence region of the solution spaces.

We discuss the coupling of fermionic fields with mass dimension one to the O'Raifeartaigh model to study supersymmetry breaking for these fermions. We find that the coupled model has two distinct solutions. The first solution represents a local minimum of the superpotential which spontaneously breaks supersymmetry in perfect analogy to the O'Raifeartaigh model. The second solution is more intriguing as it corresponds to a global minimum of the superpotential. In this case, the coupling to the fermionic sector restores supersymmetry. However, this is achieved at the cost of breaking Lorentz invariance. Finally, the mass matrices for the multiplets of the coupled model are presented. It turns out that it contains two bosonic triplets and one fermionic doublet which are mass multiplets. In addition, it contains a massless fermionic doublet as well as one fermionic triplet which is not a mass multiplet but rather an interaction multiplet that contains component fields of different mass dimension.

The results also imply that the presented model for fermionic fields with mass dimension one is an interesting candidate for supersymmetric dark matter (DM).

We introduce the Triangular Ring (TR) resonator. We show that the difference between the clockwise and anti-clockwise resonant frequencies of a vacuum TR resonator is sensitive to the birefringence parity-odd parameters of the photon's sector of the minimal Standard Model Extension (mSME): the Standard Model plus all the perturbative parameters encoding the break of the Lorentz symmetry. We report that utilizing the current technology allows for direct measurement of these parameters with a sensitivity of the parity-even ones and improves the best current resonator bounds by couple of orders of magnitudes.

We note that, designing an optical table that rotates perpendicular to the gravitational equipotential surface (geoid) allows for direct measurement of the constancy of the light speed at the vicinity of the earth in all directions, in particular, perpendicular to the geoid. If this table could achieve the precision of the ordinary tables, then it would improve the GPS bounds on the constancy of the light speed perpendicular to geoid by about eight orders of magnitude.

In this paper, we study spontaneous symmetry breaking of gauge theories in a Lorentz violating background. Here, Lorentz symmetry will be broken down to its subgroup using the formalism of very special relativity. The breaking of the Lorentz symmetry will modify the gauge theories, and this will in turn modify the Higgs mechanisms for such theories. We will explicitly demonstrate that the different Hilbert spaces in various gauges of this theory can be related to each other through the gaugeon formalism. We will also discuss the FFBRST transformation for this theory, and observe that gaugeon formalism can be obtained from same. Thus, by making the BRST parameter finite and field dependent, we can relate different Hilbert spaces in different gauges for a gauge theory with spontaneous symmetry breaking in VSR.

Lorentz symmetry is one of the fundamental symmetries of nature; however, it can be broken by several proposals such as quantum gravity effects, low energy approximations in string theory and dark matter. In this paper, Lorentz symmetry is broken in supersymmetric quantum electrodynamics using aether superspace formalism without breaking any supersymmetry. To break the Lorentz symmetry in three-dimensional quantum electrodynamics, we must use the $N=1$ aether superspace. A new constant vector field is introduced and used to deform the deformed generator of supersymmetry. This formalism is required to fix the unphysical degrees of freedom that arise from the quantum gauge transformation required to quantize this theory. By using Yokoyama’s gaugeon formalism, it is possible to study these gaugeon transformations. As a result of the quantum gauge transformation, the supersymmetric algebra gets modified and the theory is invariant under BRST symmetry. These results could aid in the construction of the Gravity’s Rainbow theory and in the study of superconformal field theory. Furthermore, it is demonstrated that different gauges in this deformed supersymmetric quantum electrodynamics can be related to each other using the gaugeon formalism.

Measurements of neutrino travel times reported last September by the OPERA collaboration have been analyzed franticly as possible evidence of superluminal propagation of a signal. Even in the likely scenario that the result ultimately does not stand up to further scrutiny, it will be worth taking notice of the few things that fundamental physics did learn in the process of studying the "OPERA anomaly".

Spontaneous breaking of Lorentz symmetry has been suggested as a possible mechanism that might occur in the context of a fundamental Planck-scale theory, such as string theory or a quantum theory of gravity. However, if Lorentz symmetry is spontaneously broken, two sets of questions immediately arise: What is the fate of the Nambu–Goldstone (NG) modes, and can a Higgs mechanism occur? A brief summary of some recent work looking at these questions is presented here.