No abstract

We consider antiPoisson superalgebras realized on the smooth Grassmann-valued functions with compact support in R n and with the grading inverse to Grassmanian parity. The lower cohomologies of these superalgebras are found. IntroductionThe odd Poisson bracket play an important role in Lagrangian formulation of the quantum theory of the gauge fields, which is known as BV-formalism The antibracket possesses many features analogous to those of the Poisson bracket and even can be obtained via "canonical formalism" with an "odd time". However, unlike the Poisson bracket, on different aspects of whose deformations (quantization) there is voluminous literature, the deformations of the antibracket is not satisfactorily studied yet. The only result is [7], where the deformations of the Poisson and antibracket superalgebras realized on the superspace of polynomials are found.The goal of present work is finding the lower cohomology spaces of antiPoisson superalgebra realized on the smooth Grassmann-valued functions with compact support in R n . These results is used in the next work [8] where the general form of the deformation of such antiPoisson superalgebra is found. Particularly, it is shown in [8] that the nontrivial deformations do exist.Let K be either R or C. We denote by D(R n ) the space of smooth K-valued functions with compact support on R n . This space is endowed with its standard topology. We set

No abstract

We derive a criterion that is convenient for applications and exactly characterizes the test function space on which the operator realization of a given series of Wick powers of a free field is possible. The suggested derivation does not use the assumption that the metric of the state space is positive and can therefore be used in a gauge theory.It is based on the systematic use of the analytic properties of the Hilbert majorant of the indefinite metric and on the application of a suitable theorem on the unconditional convergence of series of boundary values of analytic functions.

We consider local martingales of exponential form M = e X or E (X) where X denotes one component of a multivariate affine process in the sense of Duffie, Filipović and Schachermayer [8]. By completing the characterization of conservative affine processes in [8, Section 9], we provide deterministic necessary and sufficient conditions in terms of the parameters of X for M to be a true martingale.2000 Mathematics Subject Classification. 60G44, 60J25, 60J75. two anonymous referees, whose insightful reports led to a considerable improvement of the present article. 1 The stochastic exponential E (X) of a semimartingale X is the unique solution of the linear SDE dE (X) t = E (X) t− dX t with E (X) 0 = 1, cf., e.g., [13, I.4.61] for more details.