21 research outputs found
Magnetic Fourier Integral Operators
In some previous papers we have defined and studied a 'magnetic'
pseudodifferential calculus as a gauge covariant generalization of the Weyl
calculus when a magnetic field is present. In this paper we extend the standard
Fourier Integral Operators Theory to the case with a magnetic field, proving
composition theorems, continuity theorems in 'magnetic' Sobolev spaces and
Egorov type theorems. The main application is the representation of the
evolution group generated by a 1-st order 'magnetic' pseudodifferential
operator (in particular the relativistic Schr\"{o}dinger operator with magnetic
field) as such a 'magnetic' Fourier Integral Operator. As a consequence of this
representation we obtain some estimations for the distribution kernel of this
evolution group and a result on the propagation of singularities
Exterior Differentials in Superspace and Poisson Brackets
It is shown that two definitions for an exterior differential in superspace,
giving the same exterior calculus, yet lead to different results when applied
to the Poisson bracket. A prescription for the transition with the help of
these exterior differentials from the given Poisson bracket of definite
Grassmann parity to another bracket is introduced. It is also indicated that
the resulting bracket leads to generalization of the Schouten-Nijenhuis bracket
for the cases of superspace and brackets of diverse Grassmann parities. It is
shown that in the case of the Grassmann-odd exterior differential the resulting
bracket is the bracket given on exterior forms. The above-mentioned transition
with the use of the odd exterior differential applied to the linear even/odd
Poisson brackets, that correspond to semi-simple Lie groups, results,
respectively, in also linear odd/even brackets which are naturally connected
with the Lie superalgebra. The latter contains the BRST and anti-BRST charges
and can be used for calculation of the BRST operator cohomology.Comment: 12 pages, LATEX 2e, JHEP format. Correction of misprints. The titles
for some references are adde
Infinitesimal deformations of a formal symplectic groupoid
Given a formal symplectic groupoid over a Poisson manifold ,
we define a new object, an infinitesimal deformation of , which can be
thought of as a formal symplectic groupoid over the manifold equipped with
an infinitesimal deformation of the Poisson bivector
field . The source and target mappings of a deformation of are
deformations of the source and target mappings of . To any pair of natural
star products having the same formal symplectic groupoid
we relate an infinitesimal deformation of . We call it the deformation
groupoid of the pair . We give explicit formulas for the
source and target mappings of the deformation groupoid of a pair of star
products with separation of variables on a Kaehler- Poisson manifold. Finally,
we give an algorithm for calculating the principal symbols of the components of
the logarithm of a formal Berezin transform of a star product with separation
of variables. This algorithm is based upon some deformation groupoid.Comment: 22 pages, the paper is reworked, new proofs are adde
Abstract composition laws and their modulation spaces
On classes of functions defined on R^2n we introduce abstract composition
laws modelled after the pseudodifferential product of symbols. We attach to
these composition laws modulation mappings and spaces with useful algebraic and
topological properties.Comment: 19 page
Abelian gauge potentials on cubic lattices
The study of the properties of quantum particles in a periodic potential
subject to a magnetic field is an active area of research both in physics and
mathematics; it has been and it is still deeply investigated. In this review we
discuss how to implement and describe tunable Abelian magnetic fields in a
system of ultracold atoms in optical lattices. After discussing two of the main
experimental schemes for the physical realization of synthetic gauge potentials
in ultracold set-ups, we study cubic lattice tight-binding models with
commensurate flux. We finally examine applications of gauge potentials in
one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
CONTEMPORARY POSSIBILITIES OF EXTRA NONSPECIFIC PROPHYLAXIS OF TICK BORN ENCEPHALITIS IN CHILDREN
The present article contains new access to encephalitis. Results of different tactics of extra nonspecific prophylaxis of tick born used in 403 patients, who applied to hospitals for help after tick bite. Efficacy of seroprophy laxis in 361 child measured. Tactics of extra chemoprophylaxis with the help of antiviral preparation anaferon infantile was offered and its efficiency was proved in 82 children. Advantages of practical appliance of chemoprophylaxis to seroimmunity were validated.Key words: tick born encephalitis, children, prophylaxis, tick, anafero