arXiv subjects
Publications and source records attributed to S. M. Kuzenko.
We review the unified description of massless spinning particles, living in spaces of constant curvature, in the framework of the pseudoclassical approach with a gauged $N$-extended worldline supersymmetry and a local $O(N)$ invariance.
We present new geometric formulations for the fractional spin particle models on the minimal phase spaces. New consistent couplings of the anyon to background fields are constructed. The relationship between our approach and previously developed anyon models is discussed.
Starting with a manifestly conformal ($O(d,2)$ invariant) mechanics model in $d$ space and 2 time dimensions, we derive the action for a massless spinning particle in $d$-dimensional anti-de Sitter space. The action obtained possesses both gauge $N$-extended worldline supersymmetry and local $O(N)$ invarince. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat space-time background for $N > 2$ (spin greater one). The original $(d+2)$-dimensional model is characterized by rather unusual property that the corresponding supersymmetry transformations do not commute with the conformal ones, in spite of the explicit $O(d,2)$ invariance of the action.
To describe a massive particle with fixed, but arbitrary, spin on $d=4$ anti-de Sitter space $M^4$, we propose the point-particle model with configuration space ${\cal M}^6 = M^{4}\times S^{2}$, where the sphere $S^2$ corresponds to the spin degrees of freedom. The model possesses two gauge symmetries expressing strong conservation of the phase-space counterparts of the second- and fourth-order Casimir operators for $so(3,2)$. We prove that the requirement of energy to have a global positive minimum $E_o$ over the configuration space is equivalent to the relation $E_o > s$, $s$ being the particle's spin, what presents the classical counterpart of the quantum massive condition. States with the minimal energy are studied in detail. The model is shown to be exactly solvable. It can be straightforwardly generalized to describe a spinning particle on $d$-dimensional anti-de Sitter space $M^d$, with ${\cal M}^{2(d-1)} = M^d \times S^{(d-2)}$ the corresponding configuration space.
We describe a Lagrangian quantization of the free massless gauge superfield theories of higher superspins both in the anti-de Sitter and flat global superspaces.
A superfield method of computing the effective potential in supersymmetric field theories is suggested. Analysis of the structure of the effective potential in the Wess-Zumino model is carried out. It is shown that the superfield effective potential is defined by three objects: kahlerian effective potential, chiral effective potential and auxiliary fields' effective potential. One-loop kahlerian effective potential is calculated using the superfield heat kernel technique. A corresponding superfield kernel is found in explicit form. Procedure for computing higher loop corrections is developed. First (two-loop) correction to chiral effective potential is found. Two-loop kahlerian effective potential is calculated.
We propose the action of d=4 Anti-de Sitter (AdS) spinning particle with arbitrary fixed quantum numbers. Regardless of the spin value, the configuration space of the model is a direct product of d=4 AdS space and two-dimensional sphere corresponds to spinning degrees of freedom. The model is an AdS counterpart of the massive spinning particle in the Minkowski space proposed earlier. Being AdS-invariant, the model possesses two gauge symmetries implying identical conservation law for AdS-counterparts of mass and spin. Two equivalent forms of the action functional, minimal and manifestly covariant, are given.
We propose the action for a massive $N$-extended superparticle with a pure (half)integer superspin $Y,~Y = 0, 1/2, 1, 3/2, \ldots$. Regardless of the superspin value, the configuration space is ${\Bbb R}^{4|4N} \times S^2$, where $S^2$ corresponds to spinning degrees of freedom. Being explicitly super-Poincaré invariant, the model possesses two gauge symmetries implying strong conservation of the squared momentum and superspin. Hamilton constrained dynamics is developed and canonical quantization is studied. For $N$ = 1 we show that the physical super wave-functions are to be on-shell massive chiral superfields. Central-charges generalizations of the model are given.