1,318 research outputs found
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
, 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, , and with dimension of
velocity. We speculate on different possibilities to relate with
fundamental constants. In particular, expression of 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
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
meson and its structure.Comment: 32 Pages, 8 Figures and 6 Table
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