744 research outputs found
Geometrical Interpretation of BRST Symmetry in Topological Yang-Mills-Higgs Theory
We study topological Yang-Mills-Higgs theories in two and three dimensions
and topological Yang-Mills theory in four dimensions in a unified framework of
superconnections. In this framework, we first show that a classical action of
topological Yang-Mills type can provide all three classical actions of these
theories via appropriate projections. Then we obtain the BRST and anti-BRST
transformation rules encompassing these three topological theories from an
extended definition of curvature and a geometrical requirement of Bianchi
identity. This is an extension of Perry and Teo's work in the topological
Yang-Mills case. Finally, comparing this result with our previous treatment in
which we used the ``modified horizontality condition", we provide a meaning of
Bianchi identity from the BRST symmetry viewpoint and thus interpret the BRST
symmetry in a geometrical setting.Comment: 16 pages, LaTeX fil
Axions in gravity with torsion
We study a scenario allowing a solution of the strong charge parity problem
via the Peccei-Quinn mechanism, implemented in gravity with torsion. In this
framework there appears a torsion-related pseudoscalar field known as
Kalb-Ramond axion. We compare it with the so-called Barbero-Immirzi axion
recently proposed in the literature also in the context of the gravity with
torsion. We show that they are equivalent from the viewpoint of the effective
theory. The phenomenology of these torsion-descended axions is completely
determined by the Planck scale without any additional model parameters. These
axions are very light and very weakly interacting with ordinary matter. We
briefly comment on their astrophysical and cosmological implications in view of
the recent BICEP2 and Planck data.Comment: 7 pages, no figures, comments and references added, published versio
On Spinors Transformations
We begin showing that for even dimensional vector spaces all
automorphisms of their Clifford algebras are inner. So all orthogonal
transformations of are restrictions to of inner automorphisms of the
algebra. Thus under orthogonal transformations and - space and time
reversal - all algebra elements, including vectors and spinors ,
transform as and for some
algebra element . We show that while under combined spinor remain in its spinor space, under or separately
goes to a 'different' spinor space and may have opposite chirality.
We conclude with a preliminary characterization of inner automorphisms with
respect to their property to change, or not, spinor spaces.Comment: Minor changes to propositions 1 and
Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles
The non-relativistic version of the multi-temporal quantization scheme of
relativistic particles in a family of non-inertial frames (see hep-th/0502194)
is defined. At the classical level the description of a family of non-rigid
non-inertial frames, containing the standard rigidly linear accelereted and
rotating ones, is given in the framework of parametrized Galilei theories. Then
the multi-temporal quantization, in which the gauge variables, describing the
non-inertial effects, are not quantized but considered as c-number generalized
times, is applied to non relativistic particles. It is shown that with a
suitable ordering there is unitary evolution in all times and that, after the
separation of center of mass, it is still possible to identify the inertial
bound states. The few existing results of quantization in rigid non-inertial
frames are recovered as special cases
On the Einstein-Weyl and conformal self-duality equations
The equations governing anti-self-dual and Einstein-Weyl conformal geometries
can be regarded as `master dispersionless systems' in four and three dimensions
respectively. Their integrability by twistor methods has been established by
Penrose and Hitchin. In this note we present, in specially adapted coordinate
systems, explicit forms of the corresponding equations and their Lax pairs. In
particular, we demonstrate that any Lorentzian Einstein-Weyl structure is
locally given by a solution to the Manakov-Santini system, and we find a system
of two coupled third-order scalar PDEs for a general anti-self-dual conformal
structure in neutral signature.This is the accepted manuscript. The final version is available at http://scitation.aip.org/content/aip/journal/jmp/56/8/10.1063/1.4927251
The relation between the model of a crystal with defects and Plebanski's theory of gravity
In the present investigation we show that there exists a close analogy of
geometry of spacetime in GR with a structure of defects in a crystal. We
present the relation between the Kleinert's model of a crystal with defects and
Plebanski's theory of gravity. We have considered the translational defects -
dislocations, and the rotational defects - disclinations - in the 3- and
4-dimensional crystals. The 4-dimensional crystalline defects present the
Riemann-Cartan spacetime which has an additional geometric property - "torsion"
- connected with dislocations. The world crystal is a model for the gravitation
which has a new type of gauge symmetry: the Einstein's gravitation has a zero
torsion as a special gauge, while a zero connection is another equivalent gauge
with nonzero torsion which corresponds to the Einstein's theory of
"teleparallelism". Any intermediate choice of the gauge with nonzero connection
A^{IJ}_\mu is also allowed. In the present investigation we show that in the
Plebanski formulation the phase of gravity with torsion is equivalent to the
ordinary or topological gravity, and we can exclude a torsion as a separate
dynamical variable.Comment: 13 pages, 2 figure
Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity
In this work we analyze the relation between the multiplicative decomposition
of the deformation gradient as a product
of the elastic and plastic factors and the theory of uniform materials. We
prove that postulating such a decomposition is equivalent to having a uniform
material model with two configurations - total and the inelastic
. We introduce strain tensors characterizing different types of
evolutions of the material and discuss the form of the internal energy and that
of the dissipative potential. The evolution equations are obtained for the
configurations and the material metric .
Finally the dissipative inequality for the materials of this type is
presented.It is shown that the conditions of positivity of the internal
dissipation terms related to the processes of plastic and metric evolution
provide the anisotropic yield criteria
A torsional completion of gravity for Dirac matter fields and its applications to neutrino oscillations
In this paper, we consider the torsional completion of gravitation for an
underlying background filled with Dirac fields, applying it to the problem of
neutrino oscillations: we discuss the effects of the induced torsional
interactions as corrections to the neutrino oscillation mechanism.Comment: 4 page
Polar Actions on Berger Spheres
The object of this article is to study a torus action on a so-called Berger sphere. We also make some comments on polar actions on naturally reductive homogeneous spaces. Finally, we prove a rigidity-type theorem for Riemannian manifolds carrying a polar action with a fix point
Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter
Torsional degrees of freedom play an important role in modern gravity
theories as well as in condensed matter systems where they can be modeled by
defects in solids. Here we isolate a class of torsion models that support
torsion configurations with a localized, conserved charge that adopts integer
values. The charge is topological in nature and the torsional configurations
can be thought of as torsional `monopole' solutions. We explore some of the
properties of these configurations in gravity models with non-vanishing
curvature, and discuss the possible existence of such monopoles in condensed
matter systems. To conclude, we show how the monopoles can be thought of as a
natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur
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