22 research outputs found
Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes
We investigate the generic 3D topological field theory within AKSZ-BV
framework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitly
cocycles of the Lie algebra of formal Hamiltonian vector fields and we argue
that the perturbative partition function gives rise to secondary characteristic
classes. We investigate a toy model which is an odd analogue of Chern-Simons
theory, and we give some explicit computation of two point functions and show
that its perturbation theory is identical to the Chern-Simons theory. We give
concrete example of the homomorphism taking Lie algebra cocycles to
Q-characteristic classes, and we reinterpreted the Rozansky-Witten model in
this light.Comment: 52 page
Quantum differential forms
Formalism of differential forms is developed for a variety of Quantum and
noncommutative situations
Differential operators on supercircle: conformally equivariant quantization and symbol calculus
We consider the supercircle equipped with the standard contact
structure. The conformal Lie superalgebra K(1) acts on as the Lie
superalgebra of contact vector fields; it contains the M\"obius superalgebra
. We study the space of linear differential operators on weighted
densities as a module over . We introduce the canonical isomorphism
between this space and the corresponding space of symbols and find interesting
resonant cases where such an isomorphism does not exist
All Stable Characteristic Classes of Homological Vector Fields
An odd vector field on a supermanifold is called homological, if
. The operator of Lie derivative makes the algebra of smooth
tensor fields on into a differential tensor algebra. In this paper, we give
a complete classification of certain invariants of homological vector fields
called characteristic classes. These take values in the cohomology of the
operator and are represented by -invariant tensors made up of the
homological vector field and a symmetric connection on by means of tensor
operations.Comment: 17 pages, references and comments adde
Lectures on conformal field theory and Kac-Moody algebras
This is an introduction to the basic ideas and to a few further selected
topics in conformal quantum field theory and in the theory of Kac-Moody
algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate
Course on Conformal Field Theory and Integrable Models (Budapest, August
1996), to appear in Springer Lecture Notes in Physic
Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions
We obtain full description of eigenvalues and eigenvectors
of composition operators Cϕ : A (R) → A (R) for a real analytic self
map ϕ : R → R as well as an isomorphic description of corresponding
eigenspaces. We completely characterize those ϕ for which Abel’s equation
f â—¦ Ï• = f + 1 has a real analytic solution on the real line. We find
cases when the operator CÏ• has roots using a constructed embedding of
Ï• into the so-called real analytic iteration semigroups.(1) The research of the authors was partially supported by MEC and FEDER Project MTM2010-15200 and MTM2013-43540-P and the work of Bonet also by GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. NN201 605340. (2) The authors are very indebted to K. Pawalowski (Poznan) for providing us with references [26,27,47] and also explaining some topological arguments of [10]. The authors are also thankful to M. Langenbruch (Oldenburg) for providing a copy of [29].Bonet Solves, JA.; Domanski, P. (2015). Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions. Integral Equations and Operator Theory. 81(4):455-482. https://doi.org/10.1007/s00020-014-2175-4S455482814Abel, N.H.: Determination d’une function au moyen d’une equation qui ne contient qu’une seule variable. In: Oeuvres Complètes, vol. II, pp. 246-248. 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Geometric quantities associated to differential operators
Denote by F_lambda the space of fields of tensor densities of weight -lambda over a manifold M.
The space D^p_{lambda,mu} of differential operators of order at most p that map F_lambda onto F_mu are modules over the Lie algebra of vector fields Vect(M). We compute all the Vect(M)-invariant mappings from D^p_{lambda,mu} onto F_nu