We consider the reduction of supersymmetry in N -extended four dimensional supergravity via the super Higgs mechanism in theories without cosmological constant. We provide an analysis largely based on the properties of long and short multiplets of Poincaré supersymmetry. Examples of the super Higgs phenomenon are realized in spontaneously broken N = 8 supergravity through the Scherk-Schwarz mec...

We show that in the supersymmetry framework described by a Poincaré superalgebra with tensorial central charges the role of generalized superconformal symmetry which contains all these central charges is played by OSp(1|2), where k = 3 for D = 4. Following [1,2] we describe the free supertwistor model for OSp(1|8). It appears that in such a scheme the tensorial central charges satisfy additiona...

We compute the complete imaginary part of the NRQCD Lagrangian at order 1/M4 in the heavy-quark mass expansion, which includes center of mass operators, and at order αs in the matching coefficients. We also compute the imaginary part of the NRQCD Lagrangian at order 1/M6 and at order αs that contributes to the S-wave and P-wave inclusive decay widths of heavy quarkonium into light hadrons at or...

This paper is devoted to a comparison between the normalized first (non-trivial) Neumann eigenvalue $|\Omega| \mu\_1(\Omega)$ for Lipschitz open set $\Omega$ in plane and Steklov $P(\Omega) \sigma\_1(\Omega)$. More precisely, we study ratio $F(\Omega):=|\Omega| \mu\_1(\Omega)/P(\Omega) We prove that this can take arbitrarily small or large values if do not put any restriction on class of sets $...

In the space H of quaternions, we investigate a natural, invariant geometry of the open, unit disc ∆H and of the open half-space H . These two domains are diffeomorphic via a Cayley-type transformation. We first study the geometrical structure of the groups of Möbius transformations of ∆H and H + and identify original ways of representing them in terms of two (isomorphic) groups of matrices wit...

The problem of determining the radiation reaction force experienced by a scalar charge moving in flat spacetime is investigated. A consistent renormalization procedure is used, which exploits the Poincaré invariance of the theory. Radiative parts of Noether quantities carried by massive scalar field are extracted. Energy-momentum and angular momentum balance equations yield Harish-Chandra equat...

In this paper, we present a version of horizontal weighted Hardy–Rellich type and Caffarelli–Kohn– Nirenberg type inequalities on stratified groups and study some of their consequences. Our results reflect on many results previously known in special cases. Moreover, a new simple proof of the Badiale–Tarantello conjecture [2] on the best constant of a Hardy type inequality is provided. We also s...