The relativistic semi-group,Lorentz group,and tachyons. II

The algebraic structure and topological properties of the hyperbolic tangent group are considered and it is proved that a group- (Lorentz-) theoretic realization will not sufficiently reflect the hyperbolic tangent group as a whole.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 89–93, May, 1976.The author wishes to express his appreciation to D. D. Ivanenko for remarks and useful criticism.     

The relativistic semigroup,the Lorentz group,and tachyons. III

The construction of a linear, isomorphic, bounded realization of a tachyon semigroup (TSG) is carried out on a dual pair of space-times in which the sought realization by a parametric group is a semigroup of relativistic endomorphisms. The found relativistic semigroup of dual space-time transformations possesses definite probability-theoretical properties.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, July, 1977.The author is indebted to D. D. Ivanenko for his discussion, attention, and support.     

Relativistic semigroup,the lorentz group,and tachyons. IV

The algebraic and topological properties of the relativistic semigroup are discussed. Its probability-theoretical features establish that the relativistic semigroup belongs to the type of complex Markov structures. From the functional point of view, the relativistic semigroup is a compact Lie semigroup which is contracting in partial spaces. Principles of measurability, observability, and stochasticity are formulated, and these lead to a space-time structure of complex Markov kind. Thus, a certain probability-theoretical gnosiology is also possible in the theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 55–58, August, 1977.I thank D. D. Ivanenko for valuable advice and numerous discussions.     

The complex Lorentz group

Russian Physics Journal -     

Strings, tachyons and deconfinement

We argue that the tachyons which exist in some string models are a signal of deconfinement. We compare the deconfinement temperature obtained from Monte Carlo calculations with some strings models.     

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     

Noncommutativity and Lorentz violation in relativistic heavy ion collisions

We show that relativistic heavy ion collisions at LHC energies could be used as an experimental probe to detect fundamental properties of spacetime long speculated about. Our results rely on the recent proposal that magnetic fields of intensity much larger than that of magnetars should be produced at the beginning of the collisions and this could have an important impact on the experimental manifestation of a noncommutative spacetime. Indeed, in the noncommutative generalization of electrodynamics the interplay between a nonzero noncommutative parameter and an external magnetic field leads us to predict the production of lepton pairs of low invariant mass by free photons (an event forbidden by Lorentz invariant electrodynamics) in relativistic heavy ion collisions at present and future available energies. This unique channel can be clearly considered as a signature of noncommutativity. On the other hand, the search for such decays is worth anyway because their absence would ameliorate of three orders of magnitude the current bound on the noncommutative parameter.     

Time ordering and the Lorentz group

A simplified definition of point local clocks and the relationship between an inertial reference frame and a class of such clocks, at rest with respect to each other, are used for an algebraic determination of the geometry of Minkowski's space-time on the set of point events. The group of all automorphisms that preserve the time ordering induced by the set of all equivalent local clocks is shown to be generated by the inhomogeneous orthochronous Lorentz group and dilatations, consistently with a well-known result of E. C. Zeeman. The existence of a universal limit velocity and of an invariant clock cone through any event is among the implications of our proof, thus effectively exploiting a suggestion due to F. Severi.     

Lorentz covariant eikonal method in magnetohydrodynamics I. The dispersion relation

A manifestly Lorentz covariant method is developed to describe wave propagation through a cold one-component plasma in arbitrary motion. The covariant eikonal method is applied to a model pulsar plasma and the dispersion relation is derived.     

Radiation of relativistic dipoles. I

In the proposed series of articles, a systematic exposition will be given of the classical theory of radiation of relativistic point dipoles. Specific examples of radiation having practical significance will also be considered. V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 60–64, February, 1993.     

On the Lorentz group SO(3,1), geometrical supersymmetric action for particles and square-root operators II. Squeezed states and relativistic wave equations

The geometrical relativistic superparticle action is analyzed from the theoretical group point of view. To this end an alternative technique of quantization, outlined by the authors in a previous work and based on the correct interpretation of the square-root Hamiltonian, is used. We show that the obtained spectrum of physical states and the Fock construction in this previous work consist of squeezed states with the even and odd representations with the lowest weights λ = 1/4 and λ= 3/4 corresponding to four possible (nontrivial) fractional representations for the group decomposition of the spin structure. The conserved currents are computed, and a new relativistic wave equation is proposed and explicitly solved for the time-dependent case. The relation between the relativistic Schrödinger equation and the time-dependent harmonic oscillator is analyzed and discussed.     

The laws of relativistic thermodynamics: I. The macroscopic quantities

The physical quantities which occur in the laws of relativistic thermodynamics are defined as statistical expressions of relativistic kinetic theory. The role of the hydrodynamic velocity field is discussed.     

One representation of the proper Lorentz group,and quaternionic analyticity

A representation of the proper Lorentz group G is considered, with operators realized as transformations of complex-valued functions of real variables x, y, z, and t. These transformations leave invariant the set of solutions of the Moisil-Fueter equation, defining quaternionic analytic functions. A subset of quaternionic analytic functions is found, which realizes irreducible representations of the group G. A slightly different representation is also considered, in the form of a transformation of functions which leaves invariant the set of solutions of the Dirac equation for a massless particle in the quaternionic form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 73–79, October, 1982.     

The relativistic symmetry group of spin and particle number

We suggest that spin and particle number are more naturally associated with the generators of a group than are spin and mass value (as is usually assumed). This is examined using the hypercomplex number formalism of relativistic physics.     

Radiation of a relativistic magneton. I

A derivation is given of the field intensities created in vacuum by a neutral, arbitrarily moving point particle possessing a proper magnetic moment. For brevity this particle is called a magneton. The field of the magneton is represented as the superposition of a convective field and a radiation field. It is shown that the radiation field possesses the characteristic properties of the field of an electromagnetic plane wave — orthogonality and transversality.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 12–16, May, 1978.The authors wish to thank Professor V. G. Bagrov for his interest in the work and for valuable remarks.     

A discussion of causality and the Lorentz group

Zeeman (1964) has shown that the group of automorphisms for the relation of causality on Minkowski space is that generated by the orthochronous Poincaré (Halpern, 1968) group and dilatations. Here we prove that the group of automorphisms that preserve the time-like vectors of Minkowski space normwise is the complete Poincaré group. We prove that the timelike structure within the null cone of a single event does define the whole structure of Minkowski space. Further, it is shown that only inertial observers can use Minkowski space to describe space-time.     

Quantum mechanics as relativistic statistics. I: The two-particle case

It is shown that non-relativistic quantum mechanics can be treated as a kind of relativistic statistical theory, which describes the indeterministic motion of classical particles. The theory is relativistic in the sense that the relativistic notion of the state and two-time equations of motion are used. The principles and relations of quantum mechanics are obtained from the principles of statistics and those of classical mechanics.     

Conservation laws for classical and relativistic collisions. I

On the basis of simple kinematic arguments it is shown that any quantity, depending only on the nature and velocity of a particle, that is conserved in a collision must, in classical mechanics, be of the form λ+Σ_iμ_iυ_i+1/2vυ ² or in relativistic mechanics of the form λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc [1−(υ ²/c ²)]^−1/2 where λ,μ _i, andν are particle parameters.     

Intersubjectivity,relativistic covariance,and conditionals: response to C. I. J. M. Stuart

A misunderstanding persists between Stuart and me, which I do my best to clarify. Bayesian inverse subjectivities versus relativistic covariance and physical intersubjectivity are discussed. A joint number of chances formalism taking care of the propagation of the probability of causes is proposed.