Massless particles in arbitrary representations of the Lorentz group

Labastida, J.M.F.

doi:10.1016/0550-3213(89)90490-2

Cited by 154 publications

(245 citation statements)

References 22 publications

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“…Second quantization of these models introduces fields of arbitrary spin, thanks to the introduction of bosonic oscillators [14,15]. Already the Lichnerowicz algebra for the osp(2|0) model implies generating functions for totally massless, symmetric, higher spin field actions.…”

Section: Discussionmentioning

confidence: 99%

“…Gauged models of this type where p = 0 and the fields X µ are purely fermionic are known to describe massless higher spin particles 2 [12]. (When (2p, Q) = (2, 0), the fields X µ carry an sp(2) index corresponding to the spinor and conformal vector oscillators first introduced by Labastida and Vasiliev to describe higher spin fields [14,15,16].) The conserved charges of the model correspond to both commuting and anti-commuting generalizations of the gradient and divergence (alias exterior derivative and codifferential) operators, along with a Lichnerowicz wave operator (the Hamilitonian), and operators that trace over indices, count indices of a given type (form or totally symmetric), multiply by metric tensors.…”

Section: Divergence DIVmentioning

confidence: 99%

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Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

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We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p + 2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p, Q) = (2, 0) corresponds to a deformed Jacobi group and describes Lichnerowicz's original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p, Q) = (0, 1) is simply the N = 1 superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p, Q) = (0, 2) model is the N = 2 supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p, Q) = (2, 1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds.

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Section: Discussionmentioning

confidence: 99%

Section: Divergence DIVmentioning

confidence: 99%

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

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“…for t > 0, due to the commutation relations (43 labeled by the Young tableau (47). In this metric-like gauge, the identification (31) holds.…”

Section: Non-local Actionsà La Macdowell and Mansourimentioning

confidence: 99%

“…This last step has never been performed explicitly for the mixedsymmetry case to our knowledge. On the other hand, in [43] Labastida introduced an explicit self-adjoint Einstein-like tensor corresponding to his field equation and conjectured that this Einstein-like tensor would provide the local constrained quadratic action for a tensor gauge field labeled by an arbitrary Young diagram.…”

Section: Local Actionsmentioning

confidence: 99%

Tensor Gauge Fields in Arbitrary Representations of GL(D, $${\mathbb{R})}$$ : II. Quadratic Actions

Bekaert

Boulanger

2007

Commun. Math. Phys.

155

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Quadratic, second-order, non-local actions for tensor gauge fields transforming in arbitrary irreducible representations of the general linear group in D-dimensional Minkowski space are explicitly written in a compact form by making use of Levi-Civita tensors. The field equations derived from these actions ensure the propagation of the correct massless physical degrees of freedom and are shown to be equivalent to non-Lagrangian local field equations proposed previously. Moreover, these actions allow a frame-like reformulationà la MacDowell-Mansouri, without any trace constraint in the tangent indices.

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“…Tensor fields in "exotic" representations of the Lorentz group, characterized by a mixed Young symmetry type [1]- [5] are important given their presence in superstring, super-gravity, and super-symmetric high spin theories. They exhibit several interesting properties, such as being dual to spin two or higher field theories or not allowing consistent self-interactions in one of the dual formulation of linearized gravity (LG) [6].…”

Section: Introductionmentioning

confidence: 99%

Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

Bizdadea

Saliu

Toma

2012

Annals of West University of Timisoara - Physics

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A particular case of interactions of a single massless tensor field with the mixed symmetry corresponding to a two-column Young diagram (k,1) with k=4, dual to linearized gravity in D=7, is considered in the context of: self-couplings, cross-interactions with a Pauli-Fierz field, crosscouplings to purely matter theories, and interactions with an Abelian 1-form. The general approach relies on the deformation of the solution to the master equation from the antifield-BRST formalism by means of the local cohomology of the BRST differential.

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Massless particles in arbitrary representations of the Lorentz group

Cited by 154 publications

References 22 publications

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Tensor Gauge Fields in Arbitrary Representations of GL(D, $${\mathbb{R})}$$ : II. Quadratic Actions

Mixed Symmetry-Tipe (k,1) Massless Tensor Fields. Consistent Interactions Of Dual Linearized Gravity

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