Lorentz-invariant Mass Research Articles

Determination of Phase Space Spectra of the Generalized Chiral Schwinger model with the Lorentz invariant Mass like Term for the Choice a − r2 = 0

We have considered the generalized version of chiral schwinger model with the Lorentz covariant masslike term for gauge field with the choice a − r2 = 0. We carry out the quantization by the canonical Dirac method of both the gauge-invariant and non-invariant version of this model to determine the phase space structure. Therefore we have shown that the gauge invariant theory has the same physical spectrum as that of the original gauge noninvariant formulation.

Schwinger model à la Very Special Relativity

In this work, we show that Lorentz invariant theories in 1+1 dimensions admit new terms inspired by Very Special Relativity (VSR) theories. We have studied the Schwinger model in VSR. We show the axial current is classically conserved in the presence of a mass term coming from the VSR invariant terms but without standard Lorentz invariant mass. Furthermore, it is shown that both the vector current as well as the axial current are modified with respect to the free case when the fermion is coupled to an external electromagnetic field due to the nonlocal operator present in the theory. The axial anomaly is computed, and we found the same standard topological invariant with a modification in the coefficient.

Structured light pulses and their Lorentz-invariant mass

The Lorentz-invariant mass and mean propagation speed have been found for structured light pulses in a vacuum considered as relativistic objects. We have solved the boundary problem for such widely known field configurations as Gauss, Laguerre–Gauss, Bessel–Gauss, Hermite–Gauss and Airy–Gauss. The pulses were taken as having a temporal envelope of finite duration. We discovered that Lorentz-invariant mass and mean propagation speed significantly depend on the spatial–temporal structure of pulses. We found that mean propagation speed is independent of the full energy of the pulse and is less than the speed of light.

Lorentz-invariant mass and entanglement of biphoton states

The concept of the Lorentz-invariant mass of a group of particles is shown to be applicable to biphoton states formed in the process of spontaneous parametric down conversion. The conditions are found when the Lorentz-invariant mass is related directly with (proportional to) the Schmidt parameter determining a high degree of entanglement of a biphoton state with respect to transverse wave vectors of emitted photons.

Invariant Mass and Propagation Speed of Light Pulses in Vacuum

The concept of the Lorentz-invariant mass of groups of photons is shown to be applicable to classical light pulses with finite sizes and duration. Diffraction of light, providing non-collinearity of the photon motion in pulses, provides also nonzero values of their Lorentz-invariant masses. By considering light pulses as relativistic objects we find that owing to diffraction and finiteness of the Lorentz-invariant mass the mean propagation speed of pulses is always smaller than the light speed c.

Diverging light pulses in vacuum: Lorentz-invariant mass and mean propagation speed

We show that the concept of the Lorentz-invariant mass of groups of particles can be applied to light pulses consisting of very large but finite numbers of noncollinear photons. Explicit expressions are found for the invariant mass of this manifold of photons for the case of diverging Gaussian light pulses propagating in vacuum. As the found invariant mass is finite, the light pulses propagate in vacuum with a speed somewhat smaller than the light speed. A small difference between the light speed and the beam-propagation velocity is found to be directly related to the invariant mass of a pulse. Focusing and/or defocusing light pulses is shown to strengthen the effect in which the pulse slows down while the pulse invariant mass increases. A scheme for measuring these quantities experimentally is proposed and discussed.

Neutrino helicity reversal and fundamental symmetries

A rather elusive helicity reversal occurs in a gedanken experiment in which a massive left-handed Dirac neutrino, traveling at a velocity u < c, is overtaken on a highway by a speeding vehicle (traveling at velocity v with u < v < c). Namely, after passing the neutrino, looking back, one would see a right-handed neutrino (which has never been observed in nature). The Lorentz-invariant mass of the right-handed neutrino is still the same as before the passing. The gedanken experiment thus implies the existence of right-handed, light neutrinos, which are not completely sterile. Furthermore, overtaking a bunch of massive right-handed Dirac neutrinos leads to gradual de-sterilization. We discuss the helicity reversal and the concomitant sterilization and de-sterilization mechanisms by way of an illustrative example calculation, with a special emphasis on massive Dirac and Majorana neutrinos. We contrast the formalism with a modified Dirac neutrino described by a Dirac equation with a pseudoscalar mass term proportional to the fifth current.

Non-local symmetries for Yang-Mills theories and their massive counterparts in two and three dimensions

We identify a non-local symmetry for Yang-Mills theories in 1+1 and 2+1 spacetime dimensions. The symmetry mixes a vector current with the gauge field. The current involved in the symmetry is required to satisfy certain constraints. The explicit solution for the current obeying these constraints, is obtained in two spacetime dimensions and in the abelian case in three dimensions. We conjecture that the current is generated from a non-local gauge and Lorentz invariant mass term in three dimensions and provide some evidence for it. We also posit a conserved current associated with the symmetry generators and derive some of its properties. In the Abelian case, we compute the symmetry algebra and show that additional symmetry generators have to be included for the algebra to close. The algebra contains an SO(2,1) subalgebra. We also comment on the implications of this symmetry for N=1 supersymmetry.

Massive cosmologies

We explore the cosmological solutions of a recently proposed extension of general relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard Friedmann-Robertson-Walker evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low-density regime each domain of the size of the inverse graviton mass has essentially non-Friedmann-Robertson-Walker. cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.

Open FRW universes and self-acceleration from nonlinear massive gravity

In the context of a recently proposed nonlinear massive gravity with Lorentz-invariant mass terms, we investigate open Friedmann-Robertson-Walker (FRW) universes driven by arbitrary matter source. While the flat FRW solutions were recently shown to be absent, the proof does not extend to the open universes. We find three independent branches of solutions to the equations of motion for the Stückelberg scalars. One of the branches does not allow any nontrivial FRW cosmologies, as in the previous no-go result. On the other hand, both of the other two branches allow general open FRW universes governed by the Friedmann equation with the matter source, the standard curvature term and an effective cosmological constant Λ± = c±mg2. Here, mg is the graviton mass, + and - represent the two branches, and c± are constants determined by the two dimensionless parameters of the theory. Since an open FRW universe with a sufficiently small curvature constant can approximate a flat FRW universe but there is no exactly flat FRW solution, the theory exhibits a discontinuity at the flat FRW limit.

Graviton mass or cosmological constant?

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local 4D Lorentz-invariant mass terms Minkowski space is unstable. The instability can develop in a time scale that is many orders of magnitude shorter than the inverse graviton mass. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions of the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change in which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or nonlocal description from a 4D point of view.

Infrared Lorentz Violation and Slowly Instantaneous Electricity

We study a modification of electromagnetism which violates Lorentz invariance at large distances. In this theory, electromagnetic waves are massive, but the static force between charged particles is Coulomb, not Yukawa. At very short distances the theory looks just like QED. But for distances larger than 1/m the massive dispersion relation of the waves can be appreciated, and the Coulomb force can be used to communicate faster than the speed of light. In fact, electrical signals are transmitted instantly, but take a time approximately 1/m to build up to full strength. After that, undamped oscillations of the electric field are set in and continue until they are dispersed by the arrival of the Lorentz-obeying part of the transmission. Experimental constraints imply that the Compton wavelength of the photon may be as small as 6000 km. This bound is weaker than for a Lorentz-invariant mass, essentially because the Coulomb constraint is removed.

Mass terms in effective theories of high density quark matter

We study the structure of mass terms in the effective theory for quasiparticles in QCD at high baryon density. To next-to-leading order in the ${1/p}_{F}$ expansion we find two types of mass terms: chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant g there is no antiparticle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.

Consistent Fujikawa regularization of the spinning string in superspace from Pauli-Villars regularization.

We use Pauli-Villars (PV) regularization of the spinning string in superspace to identify those Fujikawa regulators which produce consistent anomalies. We use a general background gauge, and obtain, after elimination of the nonpropagating fields and using a super-Einstein and Lorentz-invariant mass term, a diagonal Fujikawa regulator with only super-Weyl anomalies. The PV extended action has extra twisted'' Becchi-Rouet-Stora-Tyutin (BRST) symmetries; dropping these, the BRST transformations of the PV fields turn into off-shell superconformal transformations plus field equations. Thus, the transformations of superconformal field theory are just on-shell BRST transformations.

A Democritean phenomenology for quantum scattering theory

The basic operational devices in a particle theory are detectors which show that a particle is “here, now” rather than “there, then.” Successful operation of these devices requires a limiting velocity. Given auxiliary devices which can change particle velocities in both magnitude and direction, the Lorentz-invariant mass can be defined. The wave-particle duality operationally required to explain the scattering of particles from a diffraction grating then predicts fluctuations in particle number (the Wick-Yukawa mechanism), if we postulate a smallest mass. We show that this suffices to establish the conventional quantum mechanical scattering formalism without postulating either “interactions” or “analyticity.” By introducing the phase change due to external electromagnetic fields, we can describe the auxiliary devices assumed above to an accuracy ofe 2/hc, thus completing the operational definition to that accuracy.