Possible Minkowskian language in two-level systems

One hundred years ago, in 1908, Hermann Minkowski completed his proof that Maxwell’s equations are covariant under Lorentz transformations. During this process, he introduced a four-dimensional space called the Minkowskian space. In 1949, P.A.M. Dirac showed the Minkowskian space can be handled with the light-cone coordinate system with squeeze transformations. While the squeeze is one of the fundamental mathematical operations in optical sciences, it could serve useful purposes in two-level systems. Some possibilities are considered in this report. It is shown possible to cross the light-cone boundary in optical and two-level systems while it is not possible in Einstein’s theory of relativity.     

Angular-momentum constraints in the light-cone quantum mechanics of the nucleon-nucleon system

We show that in the framework of the light-cone quantum mechanics of the two-nucleon system the constraints due to angular-momentum conservation can be reconstructed from the requirement of Lorentz invariance of the on-mass-shell scattering amplitudes. We have reduced the problem to the analysis of the rotational invariance of a Lippmann-Schwinger type equation and we show that, under plausible assumptions, maintaining rotational invariance of the scattering amplitude requires the two-body potential to be rotationally invariant.Work supported in part by Research Program CPBP 01.03     

The relationship between the conformal and gravitational anomalies

It is shown that the vectorial part of the general coordinate transformation (GCT) anomaly cannot be eliminated by local counterterms without generating the conformal anomaly for the system with classical GCT and conformal symmetries. The vectorial part of the GCT anomaly is equivalent to the non-topological conformal anomaly similarly as the chiral part of the GCT anomaly is equivalent to the topological Lorentz anomaly. In two dimensions, the conformal anomaly is topological, and equivalent to the Lorentz anomaly up to the factor i for the left (or right) part contribution only.     

一种Lorentz引力规范理论的正则形式

本文选择了一个特殊的、在任意座标变换下及局部Lorentz变换下不变的Lagrangian,着重讨论了在经典意义下的运动方程、给出了与Lagrangian相应的正则形式。 关键词：     

Voigt kinematics and electrodynamic consequences

It has been established that the kinematics of the Voigt transformation, which lacks group structure, is different from that of the Lorentz transformation, and that the apparent kinematic asymmetry of the Voigt coordinate transformations may be understood as a conformally symmetric kinematics. Phenomena such as the kinetic energy of a moving body and the Doppler effect are not quite the same under the conformal Voigt transformation as they are for the usual theory developed with respect to the Lorentz group. Yet the massenergy conservation law under the Voigt coordinate transformations and the mass-energy conservation law under the group of Lorentz transformations are identically the same.     

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang–Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.     

On the light-cone formulation of classical non-abelian gauge theory

For a classical Yang-Mills field which is periodic in the longitudinal light-cone coordinate: (a) a gauge condition is formulated, (b) the presence of field singularities in this gauge is shown, and (c) the relevance of these singularities to the topological charge is demonstrated.Also of the Science Sector, UNESCO     

狭义相对论中没有“矛盾方程”

根据洛伦兹变换把两个惯性系的坐标原点的时空坐标从一个坐标系变换到另一坐标系,从相对运动的角度说明洛伦兹变换是自洽的,运动物体上发生的自然过程比起静止物体的过程延缓了,并且两个坐标系中的观察者都认为对方的时钟变慢,是“动钟变慢”而非“动钟变快”,不会导致“矛盾方程”,不能混淆同一事件的变换规律与两个事件的变换结果．     

Light cone and mass shells

We propose a hypothesis which generalizes the notion of duality to off-mass-shell current matrix elements. The hypothesis, referred to as strong light-cone dominance, is formulated in terms of the light-cone sum rules, which reflect causality and the light-cone structure of current commutators: We postulate that these sum rules are saturated quasilocally by individual resonance peaks, in a similar manner as duality requires resonances to saturate the FESR for the hadronic on-shell amplitudes. This reconstitutes scaling in an average sense in regions where the leading light-cone singularity does not dominate. In coordinate space this hypothesis implies that the leading light-cone singularity regulates (tames) the entire light-cone expansion in a neighbourhood of the surface of the light-cone, whose extension is of the order of an inverse mass difference between consecutive resonances. We investigate the hypothesis of strong light-cone dominance in the framework of narrow resonance models for the vertex and show that the leading light-cone singularity indeed normalizes the single particle contributions by means of a relation of the Drell-Yan-West type. A simple Veneziano-like vertex model is exhibited, which is strongly light-cone dominated. Furthermore, we show how to exploitthe hypothesis in a rather model-independent way. We present some applications to the non-forward four-point function and show in particular that strong light-cone dominancerequires scaling for exclusive electroproduction processes like $\text{γ}{}^1\text{+}\text{N}\text{→ π +}\text{N}$.     

q-deformed Minkowski space based on a q-Lorentz algebra

The Hilbert space representations of a non-commutative -deformed Minkowski space, its momenta and its Lorentz boosts are constructed. The spectrum of the diagonalizable space elements shows a lattice-like structure with accumulation points on the light-cone. Received: 23 January 1997 / Published online: 10 March 1998     

Electrodynamics of the Maxwell-Lorentz type in the ten-dimensional space of the testing of special relativity: A case for Finsler type connections

It has recently been shown by Vargas, ⁽⁴⁾ that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one particle).In this paper, two different (families of) electrodynamics are constructed in ten-dimensional space upon the coordinate free form of the Maxwell and Lorentz equations. The two possibilities arise from the two different assumptions that one can naturally make with respect to the acceleration fields of charges, when these fields are related to their relativistic counterparts. Both theories present unattractive features, which indicates that the Maxwell-Lorentz framework is unsuitable for the construction of an electrodynamics for the Robertson test theory of the Lorentz transformations. It is argued that this construction would first require the formulation of Maxwell-Lorentz electrodynamics in the form of a connection in Finsler space. If such formulation is possible, the sought generalization would consist in simply changing bases in the tangent spaces of the manifold that supports the connection. In addition, the number of dimensions of the space of the Robertson transformations would be ten, but not greater than ten.     

N = 4 Yang-Mills theory on the light cone

The 10-dimensional supersymmetric Yang-Mills theory is constructed in the light-cone gauge. When the theory is dimensionally reduced to four dimensions it is shown that the corresponding N = 4 theory is conveniently described in terms of a scalar superfield. This formalism avoids the problem of auxiliary fields but is Lorentz invariant only on the mass shell. Similar formalisms in terms of scalar superfields are also sketched for the other supersymmetric Yang-Mills as well as for N = 8 supergravity.     

Propagation of a relativistic particle in terms of the unitary irreducible representations of the Lorentz group

In a generalized Heisenberg/Schr?dinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the particle may be defined as space-time transition between states with equal eigenvalues of the first and second Casimir operators of the Lorentz algebra. In addition we use a vector on the light-cone. A massive relativistic particle with spin 0 is considered. We also consider the nonrelativistic limit. Received: 20 September 2001 / Published online: 23 November 2001     

String Lorentz algebras outside the critical dimension?

Three recently proposed new string theories have the paradoxical property of being very similar to the Neveu-Schwarz-Ramond (NRS) model in the light-cone gauge, but having the wrong space-time dimensions. Inspired by this suggestion we examine whether Lorentz algebras can be constructed outside their usual critical dimension, by considering the lowest states of the Veneziano and NSR models, and using the complete set of operators that can be constructed out of products of oscillators.     

Area-preserving diffeomorphisms and supermembrane Lorentz invariance

The Lie algebra of area-preserving diffeomorphisms on closed membranes of arbitrary topology is investigated. On the basis of a harmonic decomposition we define the structure constants as well as two other tensors which appear in the supermembrane Lorentz generators. We derive certain identities between these tensors and analyze their validity when the areapreserving diffeomorphisms are approximated bySU(N). One of the additional tensors can then be identified with the invariant symmetric three-index tensor ofSU(N), while the second has no obvious analog. We prove that the Lorentz generators are classically conserved in the light-cone gauge for arbitrary membrane topology, as a consequence of these tensor identities. This formulation allows a systematic study of the violations of Lorentz invariance in theSU(N) approximation.     

Metric of a tidally distorted nonrotating black hole

The metric of a tidally distorted, nonrotating black hole is presented in a light-cone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The metric is expressed as an expansion in powers of r/R<1, where r is a measure of distance from the black hole and R is the local radius of curvature of the external spacetime; this is assumed to be much larger than M, the mass of the black hole. The metric is calculated up to a remainder of order (r/R)4, and it depends on a family of tidal gravitational fields which characterize the hole's local environment. The coordinate system allows an easy identification of the event horizon, and expressions are derived for its surface gravity and the rates at which the tidal interaction transfers mass and angular momentum to the black hole.     

Lattice spinor gravity

We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric arises as a composite field. Our lattice model involves no signature for space and time, describing simultaneously a Minkowski or euclidean theory. It is invariant both under Lorentz transformations and euclidean rotations. The difference between space and time arises from expectation values of composite fields. Our formulation includes local gauge symmetries beyond the generalized Lorentz symmetry. The lattice construction can be employed for formulating models with local gauge symmetries purely in terms of fermions.