Spontaneous Breakdown Of Lorentz Symmetry Research Articles

ADM energy and infra-gravitons

In QED and QCD [1, 2], infrared photons and gluons alter the Hilbert space of the theory so that the in and out states live in a Hilbert space carrying a representation of basic commutation relations which is non-equivalent to the standard Fock representation, leading to spontaneous breakdown of Lorentz symmetry and physical effects. These results are generalized here to quantum gravity regarded as an SL(2; C) gauge theory and the shift of the ADM energy density and mass from infrared spin connection (the spin cloud) is discussed.

Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives

Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar field and the vector potential is constructed in the leading order saddle point expansion. This vacuum breaks the global gauge and Lorentz symmetry spontaneously. The unitarity of time evolution is assured in the physical, positive norm subspace and the linearized equations of motion are calculated. Goldstone theorem always keeps the radiation field massless. A particular model is constructed where the the full set of standard Maxwell equations is recovered on the tree level thereby relegating the effects of broken Lorentz symmetry to the level of radiative corrections.

Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane-world scenarios

In whatever Lorentz invariant theory, the presence of extended d-dimensional objects inside a higher dimensional bulk space-time, like for instance D-branes in string theories, induces a spontaneous breakdown of the Poincare' invariance of the bulk; however the effective action describing these extended objects should still respect this larger invariance through a non-linear realization of the full symmetry. Here the specific form of such a realization in presence of an electromagnetic field is uncovered. The Dirac-Born-Infeld type action for a D-brane turns out to be invariant under such transformations. Conversely it is explicitly demonstrated in some simple cases that the most general invariant action, as long as derivatives of the field strength (and second derivatives of the scalars) can be neglected, is a linear combination of terms of the Dirac-Born-Infeld type with different scale parameters. The string result is obtained if one further assumes that the theory depends upon a single length scale.

Spontaneous breakdown of Lorentz symmetry in a simplified IKKT matrix model

Spontaneous breakdown of Lorentz symmetry in a simplified IKKT matrix model

Improved perturbation method and its application to the IIB matrix model

We present a new scheme for extracting approximate values in “the improved perturbation method”, which is a sort of resummation technique capable of evaluating a series outside the radius of convergence. We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the “plateau” structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively. We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space–time extent. In the present analysis, we find an SO ( 10 ) -symmetric vacuum besides the SO ( 4 ) - and SO ( 7 ) -symmetric vacua that have been observed. It is also found that there are two distinct SO ( 4 ) -symmetric vacua that have almost the same value of free energy but the extent of space–time is different. From the approximate values of free energy, we conclude that the SO ( 4 ) -symmetric vacua are most preferred among those three types of vacua.

On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super SU(N) Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas, Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D IIB matrix model.

Lorentz invariance and origin of symmetries.

We reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can be imposed only in the sense that all Lorentz noninvariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. The application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads to the appearance of a symmetry and, what is more, to the massless vector fields gauging this symmetry in both Abelian and non-Abelian cases. In contrast, purely global symmetries are generated only as accidental consequences of the gauge symmetry.

Spontaneously generated gauge invariance

We argue that the non-observability of the spontaneous breakdown of Lorentz symmetry (SBLS) caused by the vacuum expectation values of vector fields could provide the origin of all internal symmetries observed. Remarkably, the application of this principle to the most general relativistically invariant Lagrangian, with arbitrary couplings for all the fields involved, leads by itself to the appearance of a symmetry and, what is more, to the massless vector field(s) gauging this symmetry. A simple model for the SBLS based on massive vector and real scalar field interactions is considered; it is found that spontaneously broken gauge symmetries could also appear, when SBLS happens and is required to be physically unobservable.

Matter interactions of a three-dimensional gauge theory

A recently introduced three-dimensional gauge theory involves a tensor field Tμν. In this paper we show how this field can interact with matter fields in a gauge-invariant fashion. The possibility of spontaneous breakdown of Lorentz symmetry is considered. An additional gauge-invariant interaction for Tμν is introduced. The field Tμν interacts with gravity; we compute the η function associated with the graviton propagator and show that it is proportional to the bilinear term in the Chem–Simons action for gravity in three dimensions.

Spontaneous breaking of Lorentz symmetry in string theory.

The possibility of spontaneous breakdown of Lorentz symmetry in string theory is explored via covariant string field theory. A potential mechanism is suggested for the Lorentz breaking that may be generic in many string theories.

New metastable states in quantum field theory

It is shown that any scalar theory with spontaneous symmetry breaking of a U(1) or SU(2) internal symmetry possesses, besides the usual asymmetric vacuums characterized by a constant value of the vacuum expectation of the field, other classically stable coordinate-dependent periodic field configurations. The quantization of these configurations leads, as in the former case, to the existence of an infinite collection of new metastable ground states for which the internal symmetry is spontaneously broken. In the special case of a U(1)-symmetric theory, which is discussed in detail, it is found to lowest order in perturbation theory that the small oscillations about these configurations consist of a massless excitation (Goldstone boson) and a massive one. Moreover, it is shown that, in spite of the fact that these classical solutions are not displacement invariant, there is no spontaneous breakdown of momentum conservation. The reason for this is that for these solutions any space translation can always be compensated by a U(1) transformation. The generator of this combined transformation can then be identified as the momentum operator, and it is shown to commute with the Hamiltonian. Nevertheless, spontaneous breakdown of Lorentz symmetry does occur and is particularly manifested in the energy-momentum relationship of the one-particle states. This breakdown of Lorentz invariance invalidates the hypothesis of the Goldstone theorem, and therefore owing to renormalization effects the Goldstone boson may acquire a mass. It is also argued that, by a proper choice of an arbitrary parameter which appears in the classical solutions, Lorentz invariance can be restored approximately. It can be shown that these solutions do not exist for groups $\mathrm{U}(N)$ with $N>2$. Another possible application of these solutions to the description of metastables phases in the Landau-Ginzburg theory of critical phenomena is suggested.