1,615 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
A Z_3-graded generalization of supermatrices
We introduce Z_3-graded objects which are the generalization of the more
familiar Z_2-graded objects that are used in supersymmetric theories and in
many models of non-commutative geometry. First, we introduce the Z_3-graded
Grassmann algebra, and we use this object to construct the Z_3-matrices, which
are the generalizations of the supermatrices. Then, we generalize the concepts
of supertrace and superdeterminant
On the Supersymplectic Homogeneous Superspace Underlying the OSp(1/2) Coherent States
In this work we extend Onofri and Perelomov's coherent states methods to the
recently introduced coherent states. These latter are shown to be
parametrized by points of a supersymplectic supermanifold, namely the
homogeneous superspace , which is clearly identified with a
supercoadjoint orbit of by exhibiting the corresponding equivariant
supermoment map. Moreover, this supermanifold is shown to be a nontrivial
example of Rothstein's supersymplectic supermanifolds. More precisely, we show
that its supersymplectic structure is completely determined in terms of
-invariant (but unrelated) K\"ahler -form and K\"ahler metric on
the unit disc. This result allows us to define the notions of a superK\"ahler
supermanifold and a superK\"ahler superpotential, the geometric structure of
the former being encoded into the latter.Comment: 19 pgs, PlainTeX, Preprint CRM-185
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
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page
Symplectic geometries on supermanifolds
Extension of symplectic geometry on manifolds to the supersymmetric case is
considered. In the even case it leads to the even symplectic geometry (or,
equivalently, to the geometry on supermanifolds endowed with a non-degenerate
Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is
proven that in the odd case there are two different scalar symplectic
structures (namely, an odd closed differential 2-form and the antibracket)
which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten
Local Differential Geometry as a Representation of the SUSY Oscillator
This work proposes a natural extension of the Bargmann-Fock representation to
a SUSY system. The main objective is to show that all essential structures of
the n-dimensional SUSY oscillator are supplied by basic differential
geometrical notions on an analytical R^n, except for the scalar product which
is the only additional ingredient. The restriction to real numbers implies only
a minor loss of structure but makes the essential features clearer. In
particular, euclidean evolution is enforced naturally by identification with
the 1-parametric group of dilations.Comment: 10 pages, late
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 Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry
In the Bargmann-Fock representation the coordinates act as bosonic
creation operators while the partial derivatives act as
annihilation operators on holomorphic -forms as states of a -dimensional
bosonic oscillator. Considering also -forms and further geometrical objects
as the exterior derivative and Lie derivatives on a holomorphic , we
end up with an analogous representation for the -dimensional supersymmetric
oscillator. In particular, the supersymmetry multiplet structure of the Hilbert
space corresponds to the cohomology of the exterior derivative. In addition, a
1-complex parameter group emerges naturally and contains both time evolution
and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe
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
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