On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds
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n Lagrangian Formulations for Arbitrary Bosonic HS Fields on Minkowski Backgrounds1 A. A. Reshetnyak Laboratory of NonLinear Media Physics, Institute of Strength Physics and Materials Science, Tomsk, 634021 Russia email: [email protected] Abstract—We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat spacetime and described by the unitary irreducible integer higherspin repre sentations of the Poincare group subject to Young tableaux Y(s1, …, sk) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2k) algebra which encodes the secondclass operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gaugeinvariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields. DOI: 10.1134/S1063779612050322 1
1. INTRODUCTION
Growth of the interest to higherspin (HS) field the ory is mainly stipulated by the hopes to reconsider the problems of an unique description of variety of elemen tary particles and all known interactions especially due to expected output of LHC on the planned capacity. Remind, that it suspects both the proof of supersymme try display, the answer on the question on existence of Higgs boson, and probably a new insight on origin of Dark Matter ([1]). Because of HS field theory is closely related to superstring theory, which operates with an infinite tower of bosonic and fermionic HS fields it can be treated as an approach to study a structure of super string theory from fieldtheoretic viewpoint. Some of the aspects of current state of HS field theory are dis cussed in the reviews [2]. The paper considers the last results of constructing Lagrangian formulations (LFs) for free integer both massless and massive mixedsym metry tensor HS fields on flat ⺢1,d – 1spacetime sub ject to arbitrary Young tableaux (YT) Y(s1, …, sk) in Fronsdal metriclike formalism within BFVBRST approach [3], and based on the results presented in [4] (see [4], for detailed bibliography). It is known that for d > 4 spacetime dimensions, there appear, besides totally symmetric irreducible representations of Poincare or (Anti)deSitter ((A)dS) algebras the mixedsymmetry representations determined by more than one spinlike parameters [5], [6]. Whereas for the former ones the LFs both for massless and massive free higherspin fields is well enough developed [7⎯11] as well as on base of BFV BRST approach, e.g. in [12–15], for the latter the 1 The article is published in the original.
problem of their fieldtheoretic description is not completely solved. So, the main result within the problem of LF for arbitrary massless mixedsymmetry HS fields on a Minkowski spacetime was obtained in [16] with use of unfolded form of equations of motion for the field in “framelike” formulation. In the “met riclike” form
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