Propagateurs et commutateurs en relativité générale

Lichnerowicz, André

doi:10.1007/bf02684612

Cited by 206 publications

(198 citation statements)

References 3 publications

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“…Lichnerowicz introduced a modified Laplacian ∆ (n) acting on n-index totally symmetric tensors [6] in order to facilitate a computation of the massive spin 2 propagator on spaces of constant curvature 8 …”

Section: Symmetric Algebras and Quantum Mechanicsmentioning

confidence: 99%

“…In particular, Lichnerowicz observed that for constant curvature backgrounds one could introduce a wave operator that generalized the Laplacian and (in some sense) commuted with the action of the divergence and gradient operators on symmetric tensors [6]. (His original motivation was a computation of the spin 2 massive propagator on these spaces.)…”

Section: Introductionmentioning

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: Symmetric Algebras and Quantum Mechanicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Hallowell

Waldron

2007

Commun. Math. Phys.

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“…Here we employ units =3 1 and the operator ᮀ is Lichnerowicz's wave operator [13]. The operators tr; div; grad; g correspond to the trace, divergence, gradient and multiplication by the metric and symmetrizing operations in the symmetric algebra formalism of [8].…”

Section: One-particle Exchangementioning

confidence: 99%

“…In general, the commutator of div and grad equals the Laplace operator plus somewhat complicated curvature terms. For constant curvature manifolds such as de Sitter space there is a beautiful simplification observed long ago in a mathematical context by Lichnerowicz [13], namely…”

Section: Appendix A: Symmetric Tensor Algebramentioning

confidence: 99%

Partially massless spin-2 electrodynamics

Deser

Waldron

2006

Phys. Rev. D

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Maximal depth, partially massless, higher spin excitations can mediate charged matter interactions in a de Sitter universe. This result is motivated by similarities between these theories and their traditional Maxwell counterpart: their propagation is lightlike and corresponds to the same Laplacian eigenmodes as the de Sitter photon; they are conformal in four dimensions; their gauge invariance has a single scalar parameter and actions can be expressed as squares of single derivative curvature tensors. We study this effect in detail for its simplest spin 2 example: It is possible to construct a natural and consistent interaction scheme with conserved vector electromagnetic currents primarily coupled to the helicity 1 partially massless modes. The resulting current-current single ''partial-photon'' exchange amplitude is the (very unCoulombic) sum of contact and shorter-range terms, so the partial photon cannot replace the traditional one, but rather modifies short range electromagnetic interactions. We also write the gauge invariant fourth-derivative effective actions that might appear as effective corrections to the model, and give their contributions to the tree amplitude.

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“…The expressions of the Laplacian acting on various tensors have been worked out in [11], and for convenience we list here the relevant expressions.…”

Section: Appendixmentioning

confidence: 99%

Geometric bounds on Kaluza–Klein masses

Mukherjee

Tabbash

2001

Eur. Phys. J. C

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We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza-Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favoured for phenomenological purposes.

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Propagateurs et commutateurs en relativité générale

Cited by 206 publications

References 3 publications

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

Partially massless spin-2 electrodynamics

Geometric bounds on Kaluza–Klein masses

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