On the Fock Transformation in Nonlinear Relativity

In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation which is revealed to be different from previous results. Contrary to the earlier version of Fock's nonlinear relativity for which plane waves cannot be described, our resulting algebra keeps invariant for any coordinate and momentum transformations the four dimensional contraction $p_{\mu} x^{\mu}$, allowing therefore to associate plane waves for free particles. As in Deformed Special Relativity, we also derive a canonical transformation with which the new coordinates and momentum satisfy the usual Poisson brackets and therefore transform like the usual Lorentz vectors. Finally, we establish the dispersion relation for Fock's nonlinear relativity.Comment: 10 pages, no figure

Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum

We present and discuss two different possibilities to construct position space version for Magueijo-Smolin (MS) doubly special relativity proposal. The first possibility is to start from ordinary special relativity and then to define conserved momentum in special way. It generates MS invariant as well as nonlinear MS transformations on the momentum space, leading to consistent picture for one-particle sector of the theory. The second possibility is based on the following observation. Besides the nonlinear MS transformations, the MS energy-momentum relation is invariant also under some inhomogeneous linear transformations. The latter are induced starting from linearly realized Lorentz group in five-dimensional position space. Particle dynamics and kinematics are formulated starting from the corresponding five-dimensional interval. There is no problem of total momentum in the theory. The formulation admits two observer independent scales, the speed of light, $c$, and $k$ with dimension of velocity. We speculate on different possibilities to relate $k$ with fundamental constants. In particular, expression of $k$ in terms of vacuum energy suggests emergence of (minimum) quantum of mass.Comment: Latex twice, 14 pages, revised in accordance with the version publishedin Phys. Rev.

Proper time and path integral representations for the commutation function

On the example of the quantized spinor field, interacting with arbitrary external electromagnetic field, the commutation function is studied. It is shown that a proper time representation is available in any dimensions. Using it, all the light cone singularities of the function are found explicitly, generalizing the Fock formula in four dimensions, and a path integral representation is constructed.Comment: 20 pages, LaTeX, uses pictex macro

Low-energy general relativity with torsion: a systematic derivative expansion

We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the invariants are new. We show that in the leading order the fermion action with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4 components of the torsion (out of the general 24) playing the role of Abelian gauge bosons. The bosonic action quadratic in torsion gives masses to those gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action of a general form containing vector-vector, axial-vector and axial-axial interactions. We present a quantum field-theoretic method to average the 4-fermion interaction over the fermion medium, and perform the explicit averaging for free fermions with given chemical potential and temperature. The result is different from that following from the "spin fluid" approach used previously. On the whole, we arrive to rather pessimistic conclusions on the possibility to observe effects of the torsion-induced 4-fermion interaction, although under certain circumstances it may have cosmological consequences.Comment: 33 pages, 1 figure. A new section, discussion and references added. Final (published) versio

Operational indistinguishably of varying speed of light theories

The varying speed of light theories have been recently proposed to solve the standard model problems and anomalies in the ultra high energy cosmic rays. These theories try to formulate a new relativity with no assumptions about the constancy of the light speed. In this regard, we study two theories and want to show that these theories are not the new theories of relativity, but only re-descriptions of Einstein's special relativity.Comment: 5 pages, 2 figures, title changed, minor changes in notations and formulae, a paragraph added, Int. J. Mod. Phys. D (in press) v

Spinor fields without Lorentz frames in curved spacetime using complexified quaternions

Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated, might be related to electromagnetism, emerges naturally.Comment: 14 pages; v2: minor corrections; v3: note added concerning unified treatment of local Lorentz transformations and local U(1) gauge transformations; v4: published in J. Math. Phys. 50 083507 (2009

On gravitational flow in the Relativistic Theory of Gravitation

A definition of the gravitational flow and a short description of the recipe of its calculation are presented.Comment: 6 page

The quantum dilogarithm and representations quantum cluster varieties

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the cluster modular groups. The examples of the latter include the classical mapping class groups of punctured surfaces. One of applications is quantization of higher Teichmuller spaces. The constructed unitary representations can be viewed as analogs of the Weil representation. In both cases representations are given by integral operators. Their kernels in our case are the quantum dilogarithms. We introduce the symplectic/quantum double of cluster varieties and related them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version. To appear in Inventiones Math. The last Section of the previous versions was removed, and will become a separate pape

Analysis of the rare semileptonic B_c \rar P(D,D_s) l^{+}l^{-}/\nu\bar{\nu} decays within QCD sum rules

Considering the gluon condensate corrections, the form factors relevant to the semileptonic rare B_c \rar D,D_s(J^{P}=0^{-}) l^{+}l^{-} with $l=\tau,\mu,e$ and B_c \rar D,D_s(J^{P}=0^{-})\nu\bar{\nu} transitions are calculated in the framework of the three point QCD sum rules. The heavy quark effective theory limit of the form factors are computed. The branching fraction of these decays are also evaluated and compared with the predictions of the relativistic constituent quark model. Analyzing of such type transitions could give useful information about the strong interactions inside the pseudoscalar $D_{s}$ meson and its structure.Comment: 32 Pages, 8 Figures and 6 Table