Massive Spinning Particle on Anti-De Sitter Space

Abstract

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 M 6 = M 4 ×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 M 2(d−1) = M d × S (d−2) the corresponding configuration space.

Conformal Invariance, N-Extended Supersymmetry and Massless Spinning Particles in Anti-De Sitter Space

“…This may be most simply done with the aid of the technique developed in Ref. [15] and described briefly in Appendix. Then L AdS takes the form…”

Holography as a gauge phenomenon in Higher Spin duality

“…In [35,36] another description of the spinning Anti-de Sitter particle was given and it was shown to reduce to a description on AdS 4 times S 2 . The four first class constraints of [35,36] are…”

“…We will be able to perform this reduction in the Higher Spin case and show that it leads to a scalar field dynamics 6 dimensions, which are split into 4 of AdS 4 and a 2-sphere S 2 for the reduced spin degrees of freedom. A specific example of this reduction to physical degrees of freedom was first presented in the spinning particles framework in the work of [35,36] which we describe first. We will then demonstrate a that a very similar reduction holds for the Fronsdal HS case [34].…”

“…AdS 4 is the physical space-time while the S 2 is used to collect the complete set of higher spin fields into a single field. In [35,36] the constraints implementing the KLSS gauge were solved. We will briefly summarize this reduction.…”

Coherent (spin-)tensor fields on D = 4 anti-de Sitter space

“…In that paper the dual space F × S 2 was identified with the phase space of the massive spinning particle on AdS space. Besides this, not long ago the lagrangian model of AdS massive spinning particle was suggested, with the physical phase space being F × S 2 [15]. Therefore, the construction of this paper may be thought of as the coordinate representation realization for the quantum theory of the model of ref.…”