Hidden Lorentz symmetry of the Hořava–Lifshitz gravity

In this Letter it is shown that the Hořava–Lifshitz gravity theory admits Lorentz symmetry preserving preferred global time foliation of the spacetime

Photon polarization and Wigner's little group

To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum $\vec{k}/|\vec{k}|$ and does not depend on the frequency $k^0$. Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.Comment: Version published in Phys. Rev. A, few typos correcte

The Bargmann representation for the quantum mechanics on a sphere

The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S^2.Comment: LaTe

Lorentz-covariant quantum mechanics and preferred frame

In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial frame. This enables to avoid the problem of a noncausal transmision of information related to breaking of the Bell's inequalities in QM. Our analysis has been focused mainly on the problem of existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. It fulfills all the requirements: it is Hermitean and covariant, it has commuting components and moreover its eigenvectors (localised states) are also covariant. We have found the explicit form of the position operator and have demonstrated that in the preferred frame our operator coincides with the Newton--Wigner one. We have also defined a covariant spin operator and have constructed an invariant spin square operator. Moreover, full algebra of observables consisting of position operators, fourmomentum operators and spin operators is manifestly Poincar\'e covariant in this framework. Our results support expectations of other authors (Bell, Eberhard) that a consistent formulation of quantum mechanics demands existence of a preferred frame.Comment: 21 pages, LaTeX file, no figure

Casimir effect for tachyonic fields

In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of Abel-Plana formula. Finaly, the Casimir energy and Casimir force as the functions of distance are obtained. In order to compare the resulting formula with the standard one, we calculate the Casimir energy and Casimir force for massive, scalar field.Comment: 7 pages, 9 figure

Relativistic ideal Fermi gas at zero temperature and preferred frame

We discuss the limit T->0 of the relativistic ideal Fermi gas of luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) based on observations of our recent paper: K. Kowalski, J. Rembielinski and K.A. Smolinski, Phys. Rev. D, 76, 045018 (2007). For bradyons this limit is in fact the nonrelativistic one and therefore it is not studied herein

Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations

We show that it is possible to define a Lorentz-covariant reduced spin density matrix for massive particles. Such a matrix allows one to calculate the mean values of observables connected with spin measurements (average polarizations). Moreover, it contains not only information about polarization of the particle but also information about its average kinematical state. We also use our formalism to calculate the correlation function in the Einstein--Podolsky--Rosen--Bohm type experiment with massive relativistic particles.Comment: 7 pages, 1 figur

Quantum Jumps on a Circle

It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop periodically in time. The discontinuous changes during the course of time in the phase representing the position of a particle can be interpreted as the quantum jumps on a circle.Comment: LaTeX, 3 PostScript figure