Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^n taking values in a Grassmann algebra are described up to an equivalence transformation. It is shown that there are additional deformations which are different from the standard Moyal bracket.
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence transformation for th
e case n=m=2. It is shown that in this case the Poisson superalgebra has an additional deformation comparing with other superdimensions (n,m).
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^2 taking values in a Grassmann algebra with N generating elements are described up to an equivalence transformation for N e 2.
We study the deformation complex of the dg wheeled properad of $mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the Grothendieck-Teichmu
ller group acts on the genus completion of that wheeled properad faithfully and essentially transitively. As a second application we classify all universal quantizations of $mathbb{Z}$-graded quadratic Poisson structures together with the underlying (so called) homogeneous formality maps.
A quark model relation between the neutron charge form factor and the N->Delta charge quadrupole form factor is used to predict the C2/M1 ratio in the N->Delta transition from the elastic neutron form factor data. Excellent agreement with the electro
-pionproduction data is found, indicating the validity of the suggested relation. The implication of the negative C2/M1 ratio for the intrinsic deformation of the nucleon is discussed.
The photon behavior in an arbitrary superposition of constant magnetic and electric fields is considered on most general grounds basing on the first principles like Lorentz- gauge- charge- and parity-invariance. We make model- and approximation-indep
endent, but still rather informative, statements about the behavior that the requirement of causal propagation prescribes to massive and massless branches of dispersion curves, and describe the way the eigenmodes are polarized. We find, as a consequence of Hermiticity in the transparency domain, that adding a smaller electric field to a strong magnetic field in parallel to the latter causes enhancement of birefringence. We find the magnetic field produced by a point electric charge far from it (a manifestation of magneto-electric phenomenon). We establish degeneracies of the polarization tensor that (under special kinematic conditions) occur due to space-time symmetries of the vacuum left after the external field is imposed.