Matrix Models and Lorentz Invariance

Cosmological Implications of a Lorentz Invariance Violating O(2) Model

We derive the free energy of a Lorentz invariance violating (LIV) O(2) model, for which a non-vanishing commutator among it's momenta is supposed. Then we investigate the possible implications of such a matter field on the time evolution of a flat FRW universe at low and high temperatures.

A Note on Spontaneously Broken Lorentz Invariance

We consider a relativistic effective field theory of vector boson whose vacuum exhibits spontaneous breaking of Lorentz invariance. We argue that a simple model of this type, considered recently by Kraus and Tomboulis, is obstructed from having a consistent ultraviolet completion according to the diagnostic recently suggested by Adams, Arkani-Hamed, Dubovsky, Nicolis, and Rattazzi.

Lorentz不变性和Nambu-Goldstone定理的自发破缺

Spontaneous Breakdown of the Lorentz Invariance and the Nambu-Goldstone Theorem

在一类三维阿贝尔规范理论中，洛伦兹不变性被动态产生的磁场自发破缺。一个原本具有拓扑质量的光子变成了无间隙的，即在{ \vec p}=0时p_0=0。事实上，光子是与洛伦兹不变性的自发破缺有关的南武-戈德斯通玻色子。虽然由两个洛伦兹助推发生器产生的对称性被打破，但似乎只有一个物理的南武-戈德斯通玻色子，即光子。证明了南武-戈德斯通定理中的沃德恒等式是光子极点饱和的.

三维规范理论中洛伦兹不变性的自发破缺

Spontaneous Breakdown of the Lorentz Invariance in Three-Dimensional Gauge Theories

在一类可重正化的三维阿贝尔规范理论中，洛伦兹不变性被动态产生的磁场$B$自发破缺。真正的基态类似于量子霍尔效应。一个原本具有拓扑质量的光子变成了无隙光子，实现了与洛伦兹不变性自发破缺相关的南武-戈德斯通玻色子的作用。利用南武-戈德斯通定理给出了洛伦兹不变性自发破缺的一个简单解释和充分条件。能量密度降低$B \not= 0$被认为主要是由于光子零点能量的偏移。帕斯科94年的比赛。

Lorentz Invariance of the Pure Spinor BRST Cohomology for the Superstring

In a previous paper, the BRST cohomology in the pure spinor formalism of the superstring was shown to coincide with the light-cone Green-Schwarz spectrum by using an SO(8) parameterization of the pure spinor. In this paper, the SO(9,1) Lorentz generators are explicitly constructed using this SO(8) parameterization, proving the Lorentz invariance of the pure spinor BRST cohomology.

NOTE ON MANIFEST LORENTZ AND GENERAL COORDINATE INVARIANCE IN DUALITY SYMMETRIC MODELS。

NOTE ON MANIFEST LORENTZ AND GENERAL COORDINATE INVARIANCE IN DUALITY SYMMETRIC MODELS.

我们考虑一个推广的二元对称模型提出的施瓦茨和森。它是基于扩大模型的动力学向量场是一个时间的局部洛伦兹框架的分量。这使得人们可以在平坦的时空中保持模型的明显的洛伦兹不变性。这个领域的存在被认为是引力相互作用的遗迹，它尊重弯曲时空中的一般坐标不变性，但打破了切空间中的局部洛伦兹对称性。

Dark Matter, Quantum Gravity, Vacuum Energy, and Lorentz Invariance

We discuss the problems of dark matter, quantum gravity, and vacuum energy within the context of a theory for which Lorentz invariance is not postulated, but instead emerges as a natural consequence in the physical regimes where it has been tested.

Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory

It is shown that the one-loop two-point amplitude in {\it Lorentz-invariant} non-commutative (NC) $ϕ^3$ theory is finite after subtraction in the commutative limit and satisfies the usual cutting rule, thereby eliminating the unitarity problem in Lorentz-non-invariant NC field theory in the approximation considered.

On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills Theory

Previously it has been shown that in spin-charge separated SU(2) Yang-Mills theory Lorentz invariance can become broken by a one-cocycle that appears in the Lorentz boosts. Here we study in detail the structure of this one-cocycle. In particular we show that its non-triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also explicitely present the finite version of the cocycle.

Nonlinear QED and Physical Lorentz Invariance

The spontaneous breakdown of 4-dimensional Lorentz invariance in the framework of QED with the nonlinear vector potential constraint A_μ^{2}=M^{2}(where M is a proposed scale of the Lorentz violation) is shown to manifest itself only as some noncovariant gauge choice in the otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All the contributions to the photon-photon, photon-fermion and fermion-fermion interactions violating the physical Lorentz invariance happen to be exactly cancelled with each other in the manner observed by Nambu a long ago for the simplest tree-order…

Extending the GKZ limit without breaking Lorentz Invariance

A scenario is presented on how to shift the predicted cutoff in the cosmic ray spectrum at 10**20 eV, called the Greisen-Zatsepin-Kuzmin limit (GKZ), to larger energies without breaking the Lorentz invariance. The formulation is based on a pseudo-complex extension of standard field theory. The dispersion relation of particles can be changed, leading to a modification of the GKZ limit. Maximal shifts are determined.

On the Lorentz-invariance of the Dyson series in theories with derivative couplings

We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $ϕ^4$ theory. We eventually give evidence that Lorentz invariance is satisfied and that usual Feynman rules can be applied to the interaction Lagrangian.

The Space-Cone Gauge, Lorentz Invariance and On-Shell Recursion for One-Loop Yang-Mills amplitudes

Recursion relations are succinctly obtained for $(++... +)$ and $(-++... +)$ amplitudes in the context of the space-cone gauge in QCD. We rely on the helicity symmetry of the problems to dictate our choices of reference twistors and the momentum shifts to complexify the amplitudes. Of great importance is the power of gauge Lorentz invariance, which is enough to determine the soft factors in the latter cases.

Lorentz and Galilei Invariance on Lattices

We show that the algebraic aspects of Lie symmetries and generalized symmetries in nonrelativistic and relativistic quantum mechanics can be preserved in linear lattice theories. The mathematical tool for symmetry preserving discretizations on regular lattices is the umbral calculus.

Can one restore Lorentz invariance in quantum N=2 string?

We consider quantum N=2 string embedded into the N=4 topological framework from the perspective of the old covariant quantisation. Making use of the causality and cyclic symmetry of tree amplitudes we argue that no Lorentz covariant boson emission vertex can be constructed within the N=4 topological formalism.

Lorentz Invariance in Chiral Kinetic Theory

We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-$\frac12$ particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling requi…

Restoring Lorentz Invariance in Classical N=2 String

We study classical N=2 string within the framework of the N=4 topological formalism by Berkovits and Vafa. Special emphasis is put on the demonstration of a classical equivalence of the theories and the construction of an action for the N=4 topological string. The SO(2,2) Lorentz invariance missing in the conventional Brink--Schwarz action for the N=2 string is restored in the N=4 topological action.

Expectation Values, Lorentz Invariance, and CPT in the Open Bosonic String

The issue of spontaneous breaking of Lorentz and CPT invariance is studied in the open bosonic string using a truncation scheme to saturate the string-field action at successively higher levels. We find strong evidence for the existence of extrema of the action with nonzero expectation values for certain fields. The Lorentz- and CPT-preserving solution previously suggested in the literature is confirmed through level 12 in the action. A family of Lorentz-breaking, CPT-preserving solutions of the equations of motion is found to persist and converge through level 18 in the action. Two sequences …

Lorentz invariance and unitarity in UV finite NCQFT

Ultraviolet finite quantum field theory on even dimensional noncommutative spacetime is formulated using coordinate coherent states. 2d spacetime is foliated into families of orthogonal, non commutative, two-planes. Lorentz invariance is recovered if one imposes a single non commutative parameter theta in the theory. Unitarity is checked at the one-loop level and no violation is found. Being UV finite NCQFT does not present any UV/IR mixing.

CPT/Lorentz Invariance Violation and Quantum Field Theory

Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed

洛伦兹不变性的自发破坏

Spontaneous Breakdown of the Lorentz Invariance

我们重新研究了带有陈-西蒙斯项的三维规范理论，其中洛仑兹不变性被动态产生的磁场自发破坏。非零磁场通过南武-戈德斯通定理导致光子零点能量的降低，这是该机制的主要部分。非对称谱流起着重要的作用。纯陈-西蒙斯理论的不稳定性也被注意到。

超对称代数与d=10超杨米尔斯的Lorentz不变性

Supersymmetry algebras and Lorentz invariance for d=10 Super Yang-Mills

我们认为，在传统的超对称性可以嵌入到最近提出的一套更一般的费米子变换[ \Ref{B} ]作为一个框架，在其中研究$d=10$超级杨米尔斯。解决方案展示，其中涉及各种数量的超对称连同其不变性组的封闭代数：9个超对称与$\GT {\times}\SO (1,1)$不变性; 8个超对称与$\SO (7){\times}\SO (1,1)$不变性; 4个超对称与$\SO (3,1){\times}\U (3)$不变性。我们以这种方式恢复所有以前已知的方法添加有限数量的玻色子辅助字段，以便部分关闭的$d=10$超代数。这些解的一个重要特征是，辅助场在剩余洛伦兹对称性下发生了非平凡的变换，尽管它们最初是作为洛伦兹标量引入的。

Quantum Gravity and Lorentz invariance violation in the Standard Model

The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently, Lorentz invariance violation by Quantum Gravity(QG) have been the source of a growing interest. However, the predictions depend on ad-hoc hypothesis and too many arbitrary parameters. Here we show that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $α$ that set the …

Lorentz Invariance Violation and Modified Hawking Fermions Tunneling from Black Strings

Recently the modified Dirac equation with Lorentz invariance violation has been proposed, which would be helpful to resolve some issues in quantum gravity theory and high energy physics. In this paper, the modified Dirac equation has been generalized in curved spacetime, and then fermion tunneling of black strings is researched under this correctional Dirac field theory. We also use semi-classical approximation method to get correctional Hamilton-Jacobi equation, so that the correctional Hawking temperature and correctional black hole's entropy are derived.

有效弦的洛伦兹不变性

Lorentz invariance of effective strings

从2+1维双势阱作用下实标量场的庞加莱不变量场论出发，导出了描述有效弦背景低能激发的集体坐标上的洛仑兹表象.在这个表示中，洛伦兹变换是以无穷级数的形式给出的，是沿着世界面的导数的幂。作用于弦世界表横向的变换涉及到一个泛维$-1$项。因此，洛伦兹不变性在长有效弦理论中成立，这是由于不相关项与描述二维自由无质量标量场的二维项之间的作用相消。(in普通特克斯，不需要大包装）

Quantum Gravity induced Lorentz invariance violation in the Standard Model:hadrons

The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently we showed that the Standard Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming from QG. All terms depend on one arbitrary parameter $α$ that set the scale of QG effects. In this paper we obtain the LIV for mesons and nucleons and apply it to study several effects, including the GZK anomaly.

Homogeneously Modified Special Relativity (HMSR) -- A new possible way to introduce an isotropic Lorentz Invariance Violation in particle Standard Model

This work explores a Standard Model (S.M.) extension possibility, that violates Lorentz invariance, preserving the space-time isotropy and homogeneity. In this sense HMSR represents an attempt to introduce an isotropic Lorentz Invariance Violation in the elementary particle S.M. The theory is constructed starting from a modified kinematics, that takes into account supposed quantum effects due to interaction with the space-time background. The space-time structure itself is modified, resulting in a pseudo-Finsler manifold. The S.M. extension here provided is inspired by the effective fields the…

Lorentz Invariance in Shape Dynamics

Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a maximal symmetry, an asymptotic symmetry, and a local invariance.

Lorentz invariance in heavy particle effective theories

Employing induced representations of the Lorentz group (Wigner's little group construction), formalism for constructing heavy particle effective Lagrangians is developed, and Lagrangian constraints enforcing Lorentz invariance of the S matrix are derived. The relationship between Lorentz invariance and reparameterization invariance is established and it is shown why a standard ansatz for implementing reparameterization invariance in heavy fermion effective Lagrangians breaks down at order 1/M^4. Formalism for fields of arbitrary spin and for self-conjugate fields is presented, and the extensio…

CPT Violation Implies Violation of Lorentz Invariance

An interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.

CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncomm…

通过非度规性的涌现最小程度地破坏洛伦兹不变性？一个视角

Violating Lorentz invariance minimally by the emergence of nonmetricity? A Perspective

本文提出应在引力的规范理论框架中理解洛伦兹不变性破坏，指出时空度量-仿射几何的非零非度规性可作为洛伦兹对称性破坏的标志。

三维规范理论中自发破缺的Lorentz不变性

Spontaneously Broken Lorentz Invariance in Three-Dimensional Gauge Theories

在一类具有裸陈-西蒙斯项的三维阿贝尔规范理论中，洛伦兹不变性被非零磁场的动力学产生自发地破坏。给出了真真空能量密度的详细计算。原本有质量的光子变得没有质量，实现了与洛伦兹不变性的自发破缺相关的南武-戈德斯通玻色子的作用。

Lorentz invariance relations for twist-3 quark distributions

We calculate twist-3 parton ditribution functions (PDFs) using cut and uncut diagrams. Uncut diagrams lead to a Dirac delta function term. No such term appears when cut diagrams are used. We show that a $δ(x)$ is necessary to satisfy the Lorentz invariance relations of twist-3 PDFs, except for the Burkhardt-Cottingham sum rule in QCD.

Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff

We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale, a physical cutoff rendering the quantum field theory finite, can be made compatible with a suppression of Lorentz invariance violations at low momenta. The fine tuning required to get this suppression and to have a light scalar particle in the spectrum is determined at one loop.

Chiral Anomaly Beyond Lorentz Invariance

The chiral anomaly in the context of an extended standard model with minimal Lorentz invariance violation is studied. Taking into account bounds from measurements of the speed of light, we argue that the chiral anomaly and its consequences are general results valid even beyond the relativistic symmetry.

Scalar Field for Breaking Lorentz and Diffeomorphism Invariance

A scalar field can be inserted in Maxwell and/or Einstein theory to effect symmetry breaking. Consequences of such a modification are discussed. Possible dynamics for the scalar field are presented.

Spontaneous Breakdown of Lorentz Invariance in IIB Matrix Model

We study the IIB matrix model, which is conjectured to be a nonperturbative definition of superstring theory, by introducing an integer deformation parameter `nu' which couples to the imaginary part of the effective action induced by fermions. The deformed IIB matrix model continues to be well-defined for arbitrary `nu', and it preserves gauge invariance, Lorentz invariance, and the cluster property. We study the model at `nu' = infinity using a saddle-point analysis, and show that ten-dimensional Lorentz invariance is spontaneously broken at least down to an eight-dimensional one. We argue th…

Restoration of Lorentz Invariance of 't Hooft-Polyakov Monopole Field

Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of 't Hooft-Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.

Lorentz Invariance and Origin of Symmetries

In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant effects caused by the spontaneous breakdown of Lorentz symmetry are physically unobservable. 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 fields gauging this symm…

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 invaria…

Two-dimensional Lorentz invariance of spherically symmetric black holes

We show that a static spherically symmetric black hole, in a generic theory of gravity with generic matter fields, has a two-dimensional Lorentz symmetry.

Recovering Lorentz Invariance of DLCQ

We propose a way to recover Lorentz invariance of the perturbative S matrix in the Discrete Light-Cone Quantization (DLCQ) in the continuum limit without spoiling the trivial vacuum.

Hamiltonian Electric/Magnetic Duality and Lorentz Invariance

In (3+1) Hamiltonian form, the conditions for the electric/magnetic invariance of generic self-interacting gauge vector actions and the definition of the duality generator are obvious. Instead, (3+1) actions are not intrinsically Lorentz invariant. Imposing the Dirac-Schwinger stress tensor commutator requirement to enforce the latter yields a differential constraint on the Hamiltonian which translates into the usual Lagrangian form of the duality invariance condition obeyed by Maxwell and Born-Infeld theories. We also discuss covariance properties of some analogous scalar models.

Diffeomorphism-invariant noncommutative gravity with twisted local Lorentz invariance

We propose a new theory of gravitation on noncommutative space-time which is invariant under the general coordinate transformations, while the local Lorentz invariance is realized as twisted gauge symmetry. Our theory is remarkably simpler compared to the existing formulations of noncommutative gravity.

Unitarity in higher-order Lorentz-invariance violating QED

The unitarity in Lorentz invariance violating QED consisting of standard fermions and higher-order photons of the Myers-Pospelov theory is studied. We find ghost states associated to the higher-order character of the theory which could render the $S$ matrix nonunitary. An explicit calculation to check perturbative unitarity in the process of electron-positron scattering is performed and it is found to be possible to preserve unitarity.

Cosmological constraints on Lorentz Invariance violation in gravity and dark matter

This brief contribution is devoted to phenomenological consequences of deviations from Lorentz invariance in gravity and dark matter. We will discuss main effects on cosmological observables and current constraints derived from astrophysical and cosmological data.

How is Lorentz Invariance encoded in the Hamiltonian?

One of the disadvantages of the Hamiltonian formulation is that Lorentz invariance is not manifest in the former. Given a Hamiltonian, there is no simple way to check whether it is relativistic or not. One would either have to solve for the equations of motion or calculate the Poisson Brackets of the Noether charges to perform such a check. In this paper we show that, for a class of Hamiltonians, it is possible to check Lorentz invariance directly from the Hamiltonian. Our work is particularly useful for theories where the other methods may not be readily available.

Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models

This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group aspects with emphasis on the possibility of emergence of Lorentz invariance at low energies. Contrarily to the perturbative expansion, where in general the Lorentz symmetry restoration is delicate and may depend on stringent fine-tuning, our results provide a more favorable scenario in the large-$N$ framework. We also consider supersymmetric extension in this non…

Spontaneous Breaking of Lorentz Invariance

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…

Phenomenology of theories of gravity without Lorentz invariance: the preferred frame case

Theories of gravitation without Lorentz invariance are candidates of low-energy descriptions of quantum gravity. In this review we will describe the phenomenological consequences of the candidates associated to the existence of a preferred time direction

Quantum Gravity, Cosmology, (Liouville) Strings and Lorentz Invariance

I review some aspects of non-critical strings in connection with Lorentz-Invariance violating approaches to quantum gravity. I also argue how non-critical strings may provide a unifying framework where string Cosmology and quantum gravity may be tackled together.

Emergent Lorentz invariance with chiral fermions

We study renormalization group flows in strongly interacting field theories with fermions that correspond to transitions between a theory without Lorentz invariance at high energies down to a theory with approximate Lorentz symmetry in the infrared. Holographic description of the strong coupling is used. The emphasis is made on emergence of chiral fermions in the low-energy theory.

On Galilean and Lorentz invariance in pilot-wave dynamics

It is argued that the natural kinematics of the pilot-wave theory is Aristotelian. Despite appearances, Galilean invariance is not a fundamental symmetry of the low-energy theory. Instead, it is a fictitious symmetry that has been artificially imposed. It is concluded that the search for a Lorentz-invariant extension is physically misguided.