2,189 research outputs found
Hidden supersymmetry and Berezin quantization of N=2, D=3 spinning superparticles
The first quantized theory of N=2, D=3 massive superparticles with arbitrary
fixed central charge and (half)integer or fractional superspin is constructed.
The quantum states are realized on the fields carrying a finite dimensional, or
a unitary infinite dimensional representation of the supergroups OSp(2|2) or
SU(1,1|2). The construction originates from quantization of a classical model
of the superparticle we suggest. The physical phase space of the classical
superparticle is embedded in a symplectic superspace
, where the inner K\"ahler supermanifold
provides
the particle with superspin degrees of freedom. We find the relationship
between Hamiltonian generators of the global Poincar\'e supersymmetry and the
``internal'' SU(1,1|2) one. Quantization of the superparticle combines the
Berezin quantization on and the conventional Dirac quantization
with respect to space-time degrees of freedom. Surprisingly, to retain the
supersymmetry, quantum corrections are required for the classical N=2
supercharges as compared to the conventional Berezin method. These corrections
are derived and the Berezin correspondence principle for underlying
their origin is verified. The model admits a smooth contraction to the N=1
supersymmetry in the BPS limit.Comment: 43 pages, LaTeX Version 2.0
The wave function of a gravitating shell
We have calculated a discrete spectrum and found an exact analytical solution
in the form of Meixner polynomials for the wave function of a thin gravitating
shell in the Reissner-Nordstrom geometry. We show that there is no extreme
state in the quantum spectrum of the gravitating shell, as in the case of
extreme black hole.Comment: 7 pages, 1 figur
A new paradigm of governance for a carbon-pricing system
Throughout its life, the United Nations has played a pioneering role in the world of ideas. COP21 – also known as Paris 2015 – shows the path for the United Nations to establish a new governance that will enforce the compliance of a new planetary carbon-pricing system. Maintaining global warming below 2 °C means implementing an efficient carbon-pricing system, supported by effective measures promoting a green energy transition. A planetary carbon governance yields a number of new insights that include the following: (1) a bonus-malus system with a fixed signal price for carbon, (2) a planetary carbon market that will gather existing regional carbon markets, (3) a hybrid carbon-pricing system linking a carbon tax and a carbon market for advanced countries and (4) a support mechanism for emerging and developing countries to assist them with a carbon-pricing system. This new governance will promote an energy transition plan. In the COP21 context, responsible policymaking requires key characteristics for the enforcement of a successful planetary carbon-pricing system
Dynamics of a thin shell in the Reissner-Nordstrom metric
We describe the dynamics of a thin spherically symmetric gravitating shell in
the Reissner-Nordstrom metric of the electrically charged black hole. The
energy-momentum tensor of electrically neutral shell is modelled by the perfect
fluid with a polytropic equation of state. The motion of a shell is described
fully analytically in the particular case of the dust equation of state. We
construct the Carter-Penrose diagrams for the global geometry of the eternal
black hole, which illustrate all possible types of solutions for moving shell.
It is shown that for some specific range of initial parameters there are
possible the stable oscillating motion of the shell transferring it
consecutively in infinite series of internal universes. We demonstrate also
that this oscillating type of motion is possible for an arbitrary polytropic
equation of state on the shell.Comment: 17 pages, 7 figure
Higher order relations in Fedosov supermanifolds
Higher order relations existing in normal coordinates between affine
extensions of the curvature tensor and basic objects for any Fedosov
supermanifolds are derived. Representation of these relations in general
coordinates is discussed.Comment: 11 LaTex pages, no figure
The existence of time
Of those gauge theories of gravity known to be equivalent to general
relativity, only the biconformal gauging introduces new structures - the
quotient of the conformal group of any pseudo-Euclidean space by its Weyl
subgroup always has natural symplectic and metric structures. Using this metric
and symplectic form, we show that there exist canonically conjugate,
orthogonal, metric submanifolds if and only if the original gauged space is
Euclidean or signature 0. In the Euclidean cases, the resultant configuration
space must be Lorentzian. Therefore, in this context, time may be viewed as a
derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some
calculations condensed; typos corrected
SUSY structures, representations and Peter-Weyl theorem for
The real compact supergroup is analized from different perspectives
and its representation theory is studied. We prove it is the only (up to
isomorphism) supergroup, which is a real form of
with reduced Lie group , and a link with SUSY structures on is established. We describe a large family of complex semisimple
representations of and we show that any -representation
whose weights are all nonzero is a direct sum of members of our family. We also
compute the matrix elements of the members of this family and we give a proof
of the Peter-Weyl theorem for
Exact Evolution Operator on Non-compact Group Manifolds
Free quantal motion on group manifolds is considered. The Hamiltonian is
given by the Laplace -- Beltrami operator on the group manifold, and the
purpose is to get the (Feynman's) evolution kernel. The spectral expansion,
which produced a series of the representation characters for the evolution
kernel in the compact case, does not exist for non-compact group, where the
spectrum is not bounded. In this work real analytical groups are investigated,
some of which are of interest for physics. An integral representation for the
evolution operator is obtained in terms of the Green function, i.e. the
solution to the Helmholz equation on the group manifold. The alternative series
expressions for the evolution operator are reconstructed from the same integral
representation, the spectral expansion (when exists) and the sum over classical
paths. For non-compact groups, the latter can be interpreted as the (exact)
semi-classical approximation, like in the compact case. The explicit form of
the evolution operator is obtained for a number of non-compact groups.Comment: 32 pages, 5 postscript figures, LaTe
Super-Poincare' algebras, space-times and supergravities (I)
A new formulation of theories of supergravity as theories satisfying a
generalized Principle of General Covariance is given. It is a generalization of
the superspace formulation of simple 4D-supergravity of Wess and Zumino and it
is designed to obtain geometric descriptions for the supergravities that
correspond to the super Poincare' algebras of Alekseevsky and Cortes'
classification.Comment: 29 pages, v2: minor improvements at the end of Section 5.
Vacuum shell in the Schwarzschild-de Sitter world
We construct the classification scheme for all possible evolution scenarios
and find the corresponding global geometries for dynamics of a thin spherical
vacuum shell in the Schwarzschild-de Sitter metric. This configuration is
suitable for the modelling of vacuum bubbles arising during cosmological phase
transitions in the early Universe. The distinctive final types of evolution
from the local point of view of a rather distant observer are either the
unlimited expansion of the shell or its contraction with a formation of black
hole (with a central singularity) or wormhole (with a baby universe in
interior).Comment: 15 pages, 8 figure
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