165 research outputs found
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
The geometry of antiferromagnetic spin chains
We construct spin chains that describe relativistic sigma-models in the
continuum limit, using symplectic geometry as a main tool. The target space can
be an arbitrary complex flag manifold, and we find universal expressions for
the metric and theta-term.Comment: 31 pages, 3 figure
Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
It is known that actions of field theories on a noncommutative space-time can
be written as some modified (we call them -modified) classical actions
already on the commutative space-time (introducing a star product). Then the
quantization of such modified actions reproduces both space-time
noncommutativity and usual quantum mechanical features of the corresponding
field theory. The -modification for arbitrary finite-dimensional
nonrelativistic system was proposed by Deriglazov (2003). In the present
article, we discuss the problem of constructing -modified actions for
relativistic QM. We construct such actions for relativistic spinless and
spinning particles. The key idea is to extract -modified actions of the
relativistic particles from path integral representations of the corresponding
noncommtative field theory propagators. We consider Klein-Gordon and Dirac
equations for the causal propagators in such theories. Then we construct for
the propagators path-integral representations. Effective actions in such
representations we treat as -modified actions of the relativistic
particles. To confirm the interpretation, we quantize canonically these
actions. Thus, we obtain the Klein-Gordon and Dirac equations in the
noncommutative field theories. The -modified action of the relativistic
spinning particle is just a generalization of the Berezin-Marinov
pseudoclassical action for the noncommutative case
Chirality and Dirac Operator on Noncommutative Sphere
We give a derivation of the Dirac operator on the noncommutative -sphere
within the framework of the bosonic fuzzy sphere and define Connes' triple. It
turns out that there are two different types of spectra of the Dirac operator
and correspondingly there are two classes of quantized algebras. As a result we
obtain a new restriction on the Planck constant in Berezin's quantization. The
map to the local frame in noncommutative geometry is also discussed.Comment: 24 pages, latex, no figure
Infinitesimal deformation quantization of complex analytic spaces
Global constructions of quantization deformation and obstructions are
discussed for an arbitrary complex analytic space in terms of adapted
(analytic) Hochschild cohomology. For K3-surfaces an explicit global
construction of a Poisson bracket is given. It is shown that the analytic
Hochschild (co)homology on a complex space has structure of coherent analytic
sheaf in each degree
Supersymmetry and localization
We study conditions under which an odd symmetry of the integrand leads to
localization of the corresponding integral over a (super)manifold. We also show
that in many cases these conditions guarantee exactness of the stationary phase
approximation of such integrals.Comment: 16 pages, LATE
Two dimensional Berezin-Li-Yau inequalities with a correction term
We improve the Berezin-Li-Yau inequality in dimension two by adding a
positive correction term to its right-hand side. It is also shown that the
asymptotical behaviour of the correction term is almost optimal. This improves
a previous result by Melas.Comment: 6 figure
Open Superstring Star as a Continuous Moyal Product
By diagonalizing the three-string vertex and using a special coordinate
representation the matter part of the open superstring star is identified with
the continuous Moyal product of functions of anti-commuting variables. We show
that in this representation the identity and sliver have simple expressions.
The relation with the half-string fermionic variables in continuous basis is
given.Comment: Latex, 19 pages; more comments added and notations are simplifie
On the correlation function of the characteristic polynomials of the hermitian Wigner ensemble
We consider the asymptotics of the correlation functions of the
characteristic polynomials of the hermitian Wigner matrices .
We show that for the correlation function of any even order the asymptotic
coincides with this for the GUE up to a factor, depending only on the forth
moment of the common probability law of entries , ,
i.e. that the higher moments of do not contribute to the above limit.Comment: 20
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