Test of special relativity and equivalence principle from neutrinoless double beta decay

We generalize the formalism for testing Lorentz invariance and the weak equivalence principle in the neutrino sector. While neutrino oscillation bounds constrain the region of large mixing of the the weak and gravitational eigenstates, we obtain new constraints on violations of Lorentz invariance and the equivalence principle from neutrinoless double beta decay. These bounds apply even in the case of no mixing and thus probe a totally unconstrained region in the parameter space. January 19, 1999     

CPT/Lorentz invariance violation and neutrino oscillation

We analyze the consequences of violation of Lorentz and CPT invariance in the massless neutrino sector by deforming the canonical anti-commutation relations for the fields. We show that, for particular choices of the deformation, oscillation between massless neutrino species takes place when only Lorentz invariance is violated. On the other hand, if both Lorentz and CPT invariances are violated, we show that there is no oscillation between massless neutrino species. Comparing with the existing experimental data on neutrino oscillations, we obtain bounds on the parameter for Lorentz invariance violation.     

Lorentz invariant exact solution of the anomalous chiral Schwinger model

We present an exact solution of the anomalous chiral Schwinger model using Fermionic variables. We implement infrared regularization by considering the model on a spatial circleS ¹. Quantum effects modify the gauge constraints through the appearance of Schwinger terms in the gauge algebra. We perform a careful analysis of the resulting second class gauge constraints by implementing Dirac's method at the quantum level and obtain the spectrum of the theory. We get a consistent unitary Lorentz invariant theory for particular values of the counterterms. We find that when we regulate the fermionic sector of the model without reference to the gauge fields Lorentz invariance requires that we add both Lorentz variant and gauge variant counterterms.     

Limits on Lorentz violation from synchrotron and inverse Compton sources

We derive new bounds on Lorentz violations in the electron sector from existing data on high-energy astrophysical sources. Synchrotron and inverse Compton data give precisely complementary constraints. The best bound on a specific combination of electron Lorentz-violating coefficients is at the 6 x 10(-20) level, and independent bounds are available for all the Lorentz-violating c coefficients at the 2 x 10(-14)level or better. This represents an improvement in some bounds by 14 orders of magnitude.     

On the spectrum of the rayleigh piston II

Building on results of an earlier paper we study the discrete spectrum of the Rayleigh piston. We first prove the absence of discrete spectrum on the subspace of odd functions everywhere in the Lorentz regime. Then we give upper bounds on the number of discrete eigenvectors as a function of the mass ratio using a variety of methods which to some degree complement each other. We also investigate the precise degree of divergence of these bounds as the mass ratio goes to infinity respectively zero.     

The runaway effect in a Lorentz gas

The Lorentz gas of charged particles in a constant and uniform electric field is studied. The gas flows through the medium of immobile, randomly distributed scatterers. Particles with velocity v suffer collisions with frequency proportional to ¦v¦ ⁿ . Forn < 0 runaway of the gas is forced by the field: the mean velocity of the flow increases without bounds. By a simple physical argument an integral relation is established between the probability of collisionless motion and the velocity distribution. It is then shown that whenn < –1 a fraction of particles moves as if the scattering centers were absent. The detailed discussion of this uncollided runaway is presented. Some qualitative features of the velocity distribution are illustrated on rigorous solutions in one dimension.     

A possible identification of x (3.45) with a “time-like” cc̄ excitation

We identify the four observed intermediate states between J/ψ and ψ′ with the four j^PC = j⁺⁺P waves of a relativistic bound state model. Assuming a point-like quark photon vertex we calculate bounds on their radiative couplings to J/ψ and ψ′ by the help of four-dimensional dipole sum rules. These bounds also imply upper bounds on the total widths.     

Lorentz violation from the Higgs portal

We study bounds and signatures of models where the Higgs doublet has an inhomogeneous mass or vacuum expectation value, being coupled to a hidden sector that breaks Lorentz invariance. This physics is best described by a low-energy effective Lagrangian in which the Higgs speed-of-light is smaller than c; such effect is naturally small because it is suppressed by four powers of the inhomogeneity scale. The Lorentz violation in the Higgs sector is communicated at tree level to fermions (via Yukawa interactions) and to massive gauge bosons, although the most important effect comes from one-loop diagrams for photons and from two-loop diagrams for fermions. We calculate these effects by deriving the renormalization-group equations for the speed-of-light of the Standard Model particles. An interesting feature is that the strong coupling dynamically makes the speed-of-light equal for all colored particles.     

Radiative effects in quantum electrodynamics with Lorentz violation

We calculate one-loop mass and vertex (at zero momentum transfer) operators of an electron in a weak background tensor field that violates Lorentz invariance. The upper bounds on the background field strength are obtained using modern experimental values of the electron mass and charge.     

Refining a relativistic,hydrodynamic solver: Admitting ultra-relativistic flows

We have undertaken the simulation of hydrodynamic flows with bulk Lorentz factors in the range 10²–10⁶. We discuss the application of an existing relativistic, hydrodynamic primitive variable recovery algorithm to a study of pulsar winds, and, in particular, the refinement made to admit such ultra-relativistic flows. We show that an iterative quartic root finder breaks down for Lorentz factors above 10² and employ an analytic root finder as a solution. We find that the former, which is known to be robust for Lorentz factors up to at least 50, offers a 24% speed advantage. We demonstrate the existence of a simple diagnostic allowing for a hybrid primitives recovery algorithm that includes an automatic, real-time toggle between the iterative and analytical methods. We further determine the accuracy of the iterative and hybrid algorithms for a comprehensive selection of input parameters and demonstrate the latter’s capability to elucidate the internal structure of ultra-relativistic plasmas. In particular, we discuss simulations showing that the interaction of a light, ultra-relativistic pulsar wind with a slow, dense ambient medium can give rise to asymmetry reminiscent of the Guitar nebula leading to the formation of a relativistic backflow harboring a series of internal shockwaves. The shockwaves provide thermalized energy that is available for the continued inflation of the PWN bubble. In turn, the bubble enhances the asymmetry, thereby providing positive feedback to the backflow.     

Lorentz violation at high energy: Concepts, phenomena, and astrophysical constraints

We consider here the possibility of quantum gravity induced violation of Lorentz symmetry (LV). Even if suppressed by the inverse Planck mass such LV can be tested by current experiments and astrophysical observations. We review the effective field theory approach to describing LV, the issue of naturalness, and many phenomena characteristic of LV. We discuss some of the current observational bounds on LV, focusing mostly on those from high energy astrophysics in the QED sector at order E/M_Planck. In this context, we present a number of new results which include the explicit computation of rates of the most relevant LV processes, the derivation of a new photon decay constraint, and modification of previous constraints taking proper account of the helicity dependence of the LV parameters implied by effective field theory.     

槽道湍流的展向振荡电磁力壁面减阻

采用直接数值模拟方法,对槽道湍流的展向振荡电磁力的减阻效果和减阻机理进行了研究,讨论了电磁力强度和振荡频率对湍流猝发事件以及壁面减阻率的影响.结果表明,电磁力强度或振荡频率变化时,湍流猝发频率和猝发强度的变化趋势是相反的,所以存在最优参数使得减阻效果最好.等价壁面展向速度可以很好地描述电磁力强度和振荡频率的变化对减阻效果的综合效应。     

Cosmic rays and the search for a Lorentz Invariance Violation

This is an introductory review about the ongoing search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultrahigh energy (UHECRs). We discuss the Greisen-Zatsepin-Kuz’min (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even at factors γ∼O(10¹¹). For heavier nuclei, the energy attenuation is even faster due to photo-disintegration, again if this process is Lorentz invariant. Hence the viability of Lorentz symmetry up to tremendous γ-factors-far beyond accelerator tests-is a central issue.Next, we comment on conceptual aspects of Lorentz Invariance and the possibility of its spontaneous breaking. This could lead to slightly particle dependent “Maximal Attainable Velocities”. We discuss their effect in decays, ?erenkov radiation, the GZK cutoff and neutrino oscillation in cosmic rays.We also review the search for LIV in cosmic γ-rays. For multi-TeV γ-rays, we encounter another possible puzzle related to the transparency of the CMB, similar to the GZK cutoff, due to electron/positron creation and subsequent inverse Compton scattering. The photons emitted in a Gamma Ray Burst occur at lower energies, but their very long path provides access to information not that far from the Planck scale. We discuss conceivable nonlinear photon dispersions based on non-commutative geometry or effective approaches.No LIV has been observed so far. However, even extremely tiny LIV effects could change the predictions for cosmic ray physics drastically.An Appendix is devoted to the recent results by the Pierre Auger Collaboration, in particular the hypothesis that nearby Active Galactic Nuclei-or objects next to them-could be the UHECR sources.     

A possible identification of x (3.45) with a “time-like” c excitation

We identify the four observed intermediate states between J/ψ and ψ′ with the four j^PC = j⁺⁺P waves of a relativistic bound state model. Assuming a point-like quark photon vertex we calculate bounds on their radiative couplings to J/ψ and ψ′ by the help of four-dimensional dipole sum rules. These bounds also imply upper bounds on the total widths.     

Letter: On the Global Hyperbolicity of Lorentz 2-Step Nilpotent Lie Groups

This work is concerned with the existence of Lorentz 2-step nilpotent Lie groups having a timelike center and which are not globally hyperbolic. Namely, we prove that any left invariant Lorentz metric with a timelike center on the Heisenberg group H ²ⁿ⁺¹ is not globally hyperbolic.     

Measuring the geometrical size of multiparticle processes

We examine the possibility of measuring the geometrical size of multiparticle processes. The mean-square impact parameter, 〈b²〉, of a process can be estimated by means of lower bounds which are determined from experiment. A bound of this type, which has been proposed by Webber, is found to be inadequate for the estimate. We propose several alternative bounds. One of them represents a considerable improvement over Webber's bound, with essentially no increase in the difficulty of the measurement. Another is a theoretically optimal bound which, however, requires an extremely high-statistics experiment. We also describe a method of deriving further bounds; and make estimates of the difference between the bounds and the true 〈b²〉.     

Possibility of precision experimental verification of time retardation in moving clocks by using coherent excitation of relativistic nuclei in a crystal

Experiments with coherent excitation of relativistic nuclei in a crystal are proposed to investigate Lorentz time retardation. At present, these experiments provide the possibility of precisely (10^?4–10^?5) verifying time retardation for clock velocities corresponding to the Lorentz factor γ～100–200 and larger.     

Hilbert space representation of an algebra of observables forq-deformed relativistic quantum mechanics

Using a representation of theq-deformed Lorentz algebra as differential operators on quantum Minkowski space, we define an algebra of observables for a q-deformed relativistic quantum mechanics with spin zero. We construct a Hilbert space representation of this algebra in which the square of the massp ² is diagonal.     

Dirac-global fits to calcium elastic scattering data in the range 21-200 MeV

We present a global relativistic optical model for p+⁴⁰Ca consisting of Lorentz scalar and vector potentials parametrized as a function of energy. The shapes chosen are Woods-Saxons for the real potentials, and a linear combination of Woods-Saxons and derivative Woods-Saxons for the imaginary potentials.