The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission ...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

The property of normality and the convolution formula are established for classical fundamental solution Cauchy problem a homogeneous ultraparabolic Kolmogorov-type equation with two groups space variables degeneration. Theorems on integral representations solutions correct solvability presented classes functions exponentially increasing as |x| → ∞ .

We study the algebraic aspects of equivariant quantum cohomology algebra of the flag manifold. We introduce and study the quantum double Schubert polynomials S̃w(x, y), which are the Lascoux– Schützenberger type representatives of the equivariant quantum cohomology classes. Our approach is based on the quantum Cauchy identity. We define also quantum Schubert polynomials S̃w(x) as the Gram–Schmidt...