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We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the (Berezin)-convolution. The present analysis is easily extended to supergeometry and to non-commutative geometry.
This Letter is based on the $kappa$-Dirac equation, derived from the $kappa$-Poincar{e}-Hopf algebra. It is shown that the $kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac osc
We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain of integra
We present few types of integral transforms and integral representations that are very useful for extending to supergeometry many familiar concepts of differential geometry. Among them we discuss the construction of the super Hodge dual, the integral
In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N=2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected sub
We introduce a new approach to find the Tomita-Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo-Martin-Schwinge