Lorentz covariant spin two superspaces

Superalgebras including generators having spins up to two and realisable as tangent vector fields on Lorentz covariant generalised superspaces are considered. The latter have a representation content reminiscent of configuration spaces of (super)gravity theories. The most general canonical supercommutation relations for the corresponding phase space coordinates allowed by Lorentz covariance are discussed. By including generators transforming according to every Lorentz representation having spin up to two, we obtain, from the super Jacobi identities, the complete set of quadratic equations for the Lorentz covariant structure constants. These defining equations for spin 2 Heisenberg superalgebras are highly overdetermined. Nevertheless, non-trivial solutions can indeed be found. By making some simplifying assumptions, we explicitly construct several classes of these superalgebras.     

A non-perturbative approach to the infrared problem in QED: Construction of charged states

A non-perturbative treatment of the infrared problem in quantum electrodynamics is presented. Starting from the local and covariant correlation functions of the Gupta-Bleuler formulation an explicit construction of the physical charged states is given. They are shown to satisfy a non-(Lorentz) covariant infrared condition, of Bloch-Nordsieck type, compatible with the Gupta-Bleuler condition (resolution of Zwanziger's paradox). The breaking of the Lorentz group in the charged sectors and its physical meaning is explained. The infrared structure of the S-matrix elements between physical charged states is shown to be that of the classical Bloch-Nordsieck factors, (proof of the Bloch-Nordsieck ansatz), and to be simply related to that calculated by using local covariant states.     

Quantum Minkowski Space and Generators of Quantum Lorentz Group

From the basic 4 × 4 R matrix associated with the quantum Lorentz group SL_q(2, C) and its various fusion matrices, the covariant differential calculus on the quantum Minkowski space and the R commutation relation for the covariant generators of quantum Lorents group are presented.     

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. Q_BRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

Are the invariance principles really truly Lorentz-covariant?

It is shown that some sections of the invariance (or symmetry) principles, such as the space reversal symmetry (or parityP) and time reversal symmetryT (of elementary particle and condensed matter physics, etc.), are not really truly Lorentz covariant and hence are dependent on the chosen inertial frame; while the world parity or the proper parityW (i.e., the spacetime reversal symmetryPT) is a truly Lorentz covariant concept, the same for all inertial observers. The basic reason for this is that in theMinkowskian space-time continuum frames of special relativity (in contrast to the space and time frames) one cannot change either space or time keeping the other one fixed and also maintain the causality requirements that all world space mappings should be timelike. Indeed, I find that the Dirac-Wigner and Lee-Yang, etc. sense of Lorentz invarianceis not in full compliance with the Einstein-Minkowskirequirements of the Lorentz covariance (in conjunction with the causality requirements) of all physical laws (i.e., the worldspaceMach principle).     

Tensor representations of conformal algebra and conformally covariant operator product expansion

A conformally covariant formulation of operator product expansion is discussed as an expansion of the product of two representations into a direct sum of irreducible representations. The basic irreducible representations are analyzed and classified. The isomorphism between the conformal algebra and the O(4, 2) algebra is used to obtain a manifestly covariant formalism. The implications of the isomorphism in the derivation of the representations is discussed. The covariant O(4, 2) formalism directly relates dominant terms to nondominant terms in the light-cone limit. The essential coincidence of the problem of a conformal covariant operator product expansion to the problem of determining the form of the three-point function is stressed, together with the relevance of a selection rule for two-point functions following from exact (not spontaneously broken) conformal covariance. The role of Ward identities in a conformal covariant scheme is pointed out, and the mathematical implications on the n-point functions from causality are described.     

Violation of causality in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Gödel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Gödel-type solution, which contains special solutions in which the essential parameter of Gödel-type geometries, \(m^2\), defines any class of homogeneous Gödel-type geometries. We show that solutions of the trigonometric and linear classes (\(m^2 < 0\) and \(m=0\)) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Gödel-type solution defines the same set of Gödel tetrads \(h_A^{~\mu }\) up to a Lorentz transformation. We also showed that the single massless scalar field generates Gödel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Gödel-type solutions makes apparent that the covariant formulation of f(T) gravity does not preclude non-local violation of causality in the form of closed time-like curves.     

On the exponential of the 2-forms in relativity

A study of intrinsic properties of proper Lorentz tensors (tensor fields defining proper Lorentz transformations at every point of space-time) is made, giving rise to their covariant decompositions. The exponential series for a generic 2-form is covariantly summed, and the resulting proper Lorentz tensor is expressed as a linear combination of the metric tensor, the 2-form, its dual and its energy tensor. Some covariant expressions for the 2-form corresponding to the logarithmic branches of a proper Lorentz tensor are given. Some properties of the Lorentz group are easily found, concerning the surjectivity, local injectivity and local inversibility of the exponential map.     

General properties of physical region spinor amplitudes

The manifestly covariant formalism for dealing with physical S-matrix elements for processes between relativistic particles of arbitrary spin is reviewed. An emphasis is made on the use of homogenous polynomial techniques. Some regularity properties of the spinor amplitudes implied by general on-shell conditions (such as Lorentz invariance and boundedness of the S-operator) are discussed. Covariant decompositions for 2-particles scattering amplitudes are derived in the framework of distribution theory.     

Metric gravitation with a two parameter family of static spherically symmetric space-times

Among the variety of all conceivable metric theories of gravitation, Lorentz curvature dynamics is the most geometric extension of Einstein's field equations to fit the solar system data. In this framework two parameters determine the asymptotic form of a static spherically symmetric space-time (without imposing Einstein's conditions); these two parameters are the active gravitational mass of the source and the PPN parameter γ. The Lorentz connection is shown to satisfy covariant evolution equations which preserve either of these two parameters; furthermore, right and left oriented space-times differ in their Lorentz connection. Deviations from the Schwarzschild character find an interpretation in terms of a new object, the Lorentz curvature energy-momentum tensor, which always vanishes identically under the restriction of Einstein's conditions. These deviations contribute strongly to the gravitational force only in the neighbourhood of the Schwarzschild sphere.     

Electrodynamics: A consequence of nonlinear realizations of the Lorentz group

Extensions from the representations of the Lorentz group to include local nonlinear diagonal transformations is sufficient to generate, via the covariant derivative, the interaction of minimal coupling. These diagonal realizations are characterized by six functions φ which must satisfy a system of transformation equations. Inequivalent categories of solutions for the φ give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two different categories of these nonlinear realizations. Within this theory, charge becomes simply the nonlinear counterpart of intrinsic spin for aparticular nonlinear realization of the Lorentz group. Charge is thus placed on equal footing with intrinsic spin in the sense that both phenomena can be described as consequences of our space-time symmetry. Other solutions for the six φ exist, including a spinor. We briefly discuss the possibility that with these other solutions, these realizations could represent some other basic properties of elementary particles.     

Radial asymptotics of Lemaître–Tolman–Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaître–Tolman–Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length ?, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular “open” LTB models whose space slices allow for a diverging ?, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as ? → ∞. The “asymptotic state” is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne’s space), sections of the Schwarzschild–Kruskal manifold or self-similar dust solutions.     

Elastic unitarity and the K-matrix in a Lorentz covariant representation of the NN interaction

A Lorentz covariant representation of the NN t-matrix has been obtaained over the energy range from 150 to 500 MeV by solving the integral equation that connects the t-matrix with the K-matrix. The K-matrix is expanded in a complete set of on-shell Lorentz invariant amplitudes represented phenomenologically by isoscalar and isovector “meson” exchanges. The real part of the K-matrix is fit over the energy range from 150 to 500 MeV using coupling strengths that are allowed to vary quadratically with energy. Above the pion production threshold at T_lab = 280 MeV, the real K-matrix is supplemented by an imaginary part with linear energy dependence. The K-matrix parameters are fit to thesmost recent (January 1999) Arndt amplitudes [R.A. Arndt, D. Roper, VPI and SU Scattering Analysis Interactive Dial-in Program and Data Base]. Direct and exchange contributions to the K-matrix are handled explicitly in the formalism. The resulting t-matrix satisfies elastic unitary below the pion production threshold and contains non-local terms that are not present in direct Love-Franey parameterizations of the t-matrix. Results are given for the NN amplitudes and compared with both the Arndt amplitudes and amplitudes obtained from a direct fit of the t-matrix [O.V. Maxwell, Nucl. Phys. A 600 (1996) 509]. Results are also given for a selected set of np and pp observables.     

Thermodynamics and Preferred Frame

The Lorentz covariant statistical physics and thermodynamics is formulated within the preferred frame approach. The transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lorentz-invariant measure on the phase space are found using Lorentz transformations in absolute synchronization. Next, the probability density and partition function are investigated using the preferred frame approach, and the transformation laws for internal energy, entropy, temperature and other thermodynamical potentials are established. The Lorentz covariance of basic thermodynamical relations, including Clapeyron's equation and Maxwell's relations is shown. Finally, the relation of presented approach to the previous approaches to relativistic thermodynamics is briefly discussed.     

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres’ theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres’ theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.     

Covariant canonical quantization of the green-schwarz superstring

Introducing a new type of D = 10 harmonic superspace with two generations of harmonic coordinates, we reduce the Green-Schwarz (GS) superstring to a system whose constraints are Lorentz covariant and functionally independent. These features allow us to impose Lorentz-covariant gauge fixing conditions for the reparametrization and the fermionic κ-invariances. The resulting Q_BRST corresponds to the finite-dimensional Lie algebra of the remaining purely harmonic constraints. The super-Poincaré symmetry acts in a manifestly Lorentz-covariant form and is apparently anomaly free.     

Bose-Einstein correlations inK + p and π+ p at 250 GeV/c

Two-pion correlations are studied for pions of like charge inK ⁺ p andπ ⁺ p collisions at 250 GeV/c. An enhanced production is observed at small momentum difference and is attributed to Bose-Einstein interference between identical particles. A systematic study is presented on the influence of parametrization and reference sample. Interpreted in terms of the Kopylov-Podgoretskii parametrization a size of the emitting regionr _K ≈1.4 fm is found. The Lorentz invariant parametrization of Goldhaber givesr _G ≈0.8 fm. With fixed parametrization, similarity is found for hadronhadron,e ⁺ e ^? and lepton-hadron collisions. No multiplicity or angular dependence is found at our energy.     

Transformation properties under broken symmetry

A general condition is derived which allows a local field (in an arbitrary field theory) to belong simultaneously to a fixed representation of the Lorentz group and a given representation of a broken symmetry group. Specializing to local currents one obtains the conditions of Gross and Jackiw for a complete current algebra, the condition of Bég et al. for the dimension of a current component to be independent of its Lorentz index, and the condition necessary for covariant derivatives in broken chiral theories to be covariant. Also, one is able to understand observation of Kimel on the failure of complete current algebra in gauge field models with mass-breaking terms, those by Takahashi and others on the impossibility of assigning a dimension to Duffin-Kemmer scalar and Klein-Gordon vector fields, and some other specific results. The above condition allows a critical examination of operator product expansions. The point of the paper is in its generality; it makes possible a unified view of a large number of specific results and observations.     

Reply to comay’s "relativity versus the longitudinal magnetic field of the photon"

Poincaré group electrodynamics is {ie255-1} conserving and Lorentz covariant under all conditions by definition. Examples are given of these properties. Comay’s comment is incorrect: any {ie255-2} conserving field theory that is Lorentz covariant is consistent with special relativity, whose underlying group is the Poincaré group.