The spinor and tensor fields with higher spin on spaces of constant curvature

Homma, Yasushi; Tomihisa, Takuma

doi:10.1007/s10455-021-09791-4

Cited by 3 publications

(7 citation statements)

References 21 publications

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“…∇ /ψ µ1...µr = iζψ µ1...µr (1.4) ∇ α ψ αµ2...µr = 0, γ α ψ αµ2...µr = 0, (1.5) where ψ µ1...µr is a totally symmetric tensor-spinor of rank r on S N which also satisfies the TT conditions (1.5) and ∇ / is the Dirac operator on S N . The eigenvalue in equation (1.4) is imaginary [15], i.e. ζ ∈ R, since, as is well known, ∇ / 2 is negative semidefinite on compact spin manifolds.…”

Section: Main Aim and Strategy Of The Present Papermentioning

confidence: 97%

“…All the χ + eigenspinors are orthogonal to all the χ − eigenspinors in equation (2.23) [38]. For each allowed value of ℓ, the eigenspinors χ +ℓ ρ and χ −ℓ ρ separately form irreducible representations of spin(N) [15]. For odd N = 2p + 1, the spinors χ +ℓ ρ (or χ −ℓ ρ) form a spin(2p + 1) representation with the (p-component) highest weight [38]…”

Section: Gamma Matrices and Tensor-spinor Fields On The N-spherementioning

confidence: 99%

“…where √ g is given by equation (2.24). For each allowed value of ℓ, the set of eigenmodes { ψ( Ã;ℓ ρ) ±θj } forms a spin(N) representation with highest weight [15]. The type-II modes ψ (II-Ã;σ;nℓ; ρ) ±µ on S N with negative (σ = −) and positive (σ = +) spin projections are given by [16] are given by equations (3.1) and (3.2), respectively.…”

Section: Stssh's Of Rank 1 For N Evenmentioning

confidence: 99%

“…. ., λ N/2 ) for this representation is given by [15] The rank-2 type-III modes are constructed using the STSSH's of rank 2 on…”

Section: Stssh's Of Rank 2 For N Evenmentioning

confidence: 99%

“…where all the ψ+θiθj modes are orthogonal to all the ψ−θiθj modes. For each value of ℓ, the set of eigenmodes { ψ( B;ℓ ρ) ±θiθj } forms a spin(N) representation with highest weight [15]:…”

Section: Stssh's Of Rank 2 For N Evenmentioning

confidence: 99%

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(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

Letsios

2024

J. Phys. A: Math. Theor.

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In our previous article [J. High Energ. Phys. 2023, 15 (2023)], we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on N-dimensional (N ≧ 3) de Sitter spacetime (dSN) are non-unitary unless N=4. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic labels that correspond to the Unitary Irreducible Representations (UIR's) of the de Sitter (dS) algebra spin(N,1) and the ones corresponding to the space of eigenmodes of the field theories. In this paper, we provide a technical representation-theoretic explanation for this fact by studying the (non-)existence of positive-definite, dS invariant scalar products for the spin-3/2 and spin-5/2 strictly/ partially massless eigenmodes on dSN (N ≧ 3). Our basic tool is the examination of the action of spin(N,1) generators on the space of eigenmodes, leading to the following findings. For odd N, any dS invariant scalar product is identically zero. For even N > 4, any dS invariant scalar product must be indefinite. This gives rise to positive-norm and negative-norm eigenmodes that mix with each other under spin(N,1) boosts. In the N=4 case, the positive-norm sector decouples from the negative-norm sector and each sector separately forms a UIR of spin(4,1). Our analysis makes extensive use of the analytic continuation of tensor-spinor spherical harmonics on the N-sphere (SN) to dSN and also introduces representation-theoretic techniques that are absent from the mathematical physics literature on half-odd-integer-spin fields on dSN.

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Section: Main Aim and Strategy Of The Present Papermentioning

confidence: 97%

Section: Gamma Matrices and Tensor-spinor Fields On The N-spherementioning

confidence: 99%

Section: Stssh's Of Rank 1 For N Evenmentioning

confidence: 99%

“…. ., λ N/2 ) for this representation is given by [15] The rank-2 type-III modes are constructed using the STSSH's of rank 2 on…”

Section: Stssh's Of Rank 2 For N Evenmentioning

confidence: 99%

Section: Stssh's Of Rank 2 For N Evenmentioning

confidence: 99%

See 3 more Smart Citations

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

Letsios

2024

J. Phys. A: Math. Theor.

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(Non-)unitarity of strictly and partially massless fermions on de Sitter space

Letsios

2023

J. High Energ. Phys.

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We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin s = 3/2, 5/2 with any mass parameter on D-dimensional (D ≥ 3) de Sitter space (dSD) and Unitary Irreducible Representations (UIR’s) of the de Sitter algebra spin(D, 1). Our approach is based on expressing the eigenmodes on global dSD in terms of eigenmodes of the Dirac operator on the (D − 1)-sphere, which provides a natural way to identify the corresponding representations with known UIR’s under the decomposition spin(D, 1) ⊃ spin(D). Remarkably, we find that four- dimensional de Sitter space plays a distinguished role in the case of the gauge-invariant theories. In particular, the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields on dSD, are not unitary unless D = 4.

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New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

Letsios

2024

J. High Energ. Phys.

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We present new infinitesimal ‘conformal-like’ symmetries for the field equations of strictly massless spin-s ≥ 3/2 totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime (dS4). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of dS4, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra so(2, 4) up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of γ5 times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities ±s of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra so(1, 4).

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The spinor and tensor fields with higher spin on spaces of constant curvature

Cited by 3 publications

References 21 publications

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

(Non-)unitarity of strictly and partially massless fermions on de Sitter space

New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

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