Related papers: Note on the super-extended Moyal formalism and its…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We introduce a doubled formalism for the bosonic sector of the maximal supergravities, in which a Hodge dual potential is introduced for each bosonic field (except for the metric). The equations of motion can then be formulated as a twisted…
It is shown that a Moyal deformation quantization of the SO(4k) Generalized Yang-Mills (GYM) theory action in D=4k dimensions, for spacetime independent field configurations, in the $\hbar \to 0$ limit, yields the Dirac-Nambu-Goto p-brane…
A modification of the harmonic superfield formalism in $D=4, N=2$ supergravity using a subsidiary condition of covariance under the background supersymmetry with a central charge ($B$-covariance) is considered. Conservation of analyticity…
Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2D Yang-Mills theories in the Schwinger--Fock gauge. Our calculation is done for arbitrary 2D…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…
We study quantisation of noncommutative gravity theories in two dimensions (with noncommutativity defined by the Moyal star product). We show that in the case of noncommutative Jackiw-Teitelboim gravity the path integral over gravitational…
We study Siegel superparticle moving in $R^{4|4}$ flat superspace. Canonical quantization is accomplished yielding the massless Wess-Zumino model as an effective field theory. Path integral representation for the corresponding…
Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the…
The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of the odd reflections for the Yangian ${\rm Y}({\frak gl}_{m|n})$ and use them…
The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…
We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory…
Moyal-deformed hierarchies of soliton equations can be extended to larger hierarchies by including additional evolution equations with respect to the deformation parameters. A general framework is presented in which the extension is…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
Gradient expansions in quantum transport equations of a Kadanoff-Baym form have been reexamined. We have realized that in a consistent approach the expansion should be performed also inside of the self-energy in the scattering integrals of…
An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry,…
Some symmetries can be broken in the quantization process (anomalies) and this breaking is signalled by a non-invariance of the quantum path integral measure. In this talk we show that it is possible to formulate also classical field…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…