Bosonic and fermionic Weinberg-Joos (j,0) ⊕ (0,j) states of arbitrary spins as Lorentz tensors or tensor-spinors and second-order theory

Acosta, E. G. Delgado; Guzman, Victor Miguel Banda; Kirchbach, Mariana

doi:10.1140/epja/i2015-15035-x

Cited by 19 publications

(33 citation statements)

References 30 publications

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“…The irreducible (3/2, 0) ⊕ (0, 3/2) building block in (4) can be singled out upon application to T µν a of a momentum independent projector, P (3/2,0) , earlier properly constructed in [13] from one of the Casimir invariants of the inhomogeneous Lorentz group algebra as,…”

Section: Introductionmentioning

confidence: 99%

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

Edwards

Kirchbach

2019

Int. J. Mod. Phys. A

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We construct the Rarita-Schwinger basis vectors, U µ , spanning the direct product space, U µ := A µ ⊗ u M , of a massless four-vector, A µ , with massless Majorana spinors, u M , together with the associated field-strength tensor, T µν := p µ U ν − p ν U µ . The T µν space is reducible and contains one massless subspace of a pure spin-3/2 ∈ (3/2, 0) ⊕ (0, 3/2). We show how to single out the latter in a unique way by acting on T µν with an earlier derived momentum independent projector, P (3/2,0) , properly constructed from one of the Casimir operators of the algebra so(1, 3) of the homogeneous Lorentz group. In this way it becomes possible to describe the irreducible massless (3/2, 0) ⊕ (0, 3/2) carrier space by means of the anti-symmetric-tensor of second rank with Majorana spinor components, defined as w (3/2,0) µν := P (3/2,0) µν γδ T γδ . The conclusion is that the (3/2, 0) ⊕ (0, 3/2) bi-vector spinor field can play the same role with respect to a U µ gauge field as the bi-vector, (1, 0) ⊕ (0, 1), associated with the electromagnetic field-strength tensor, F µν , plays for the Maxwell gauge field, A µ . Correspondingly, we find the free electromagnetic field equation, p µ F µν = 0, is paralleled by the free massless Rarita-Schwinger field equation, p µ w (3/2,0) µν = 0, supplemented by the additional condition, γ µ γ ν w (3/2,0) µν = 0, a constraint that invokes the Majorana sector.

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Section: Introductionmentioning

confidence: 99%

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

Edwards

Kirchbach

2019

Int. J. Mod. Phys. A

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“…Such an 8-dimensional spinor representation is not the popular choice because it cannot be written in a covariant form. As a consequence it is hard to construct the corresponding interaction Lagrangian.Fortunately, Acosta et al [12] show that the components of the 8-dimensional spinor can be embedded into a totally antisymmetric tensor of second rank. The representation is called the antisymmetric tensor spinor (ATS) representation, which is formed by the tensor product of an antisymmetric tensor and the Dirac field.…”

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confidence: 99%

“…Fortunately, Acosta et al [12] show that the components of the 8-dimensional spinor can be embedded into a totally antisymmetric tensor of second rank. The representation is called the antisymmetric tensor spinor (ATS) representation, which is formed by the tensor product of an antisymmetric tensor and the Dirac field.…”

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Pure spin-3/2 propagator for use in particle and nuclear physics

2017

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We propose the use of pure spin-3/2 propagator in the (3/2, 0) ⊕ (0, 3/2) representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the ∆ resonance contribution to the elastic πN scattering as an example. We find that the use of conventional gauge invariant interaction Lagrangian leads to a problem; the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of Rarita-Schwinger we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.PACS numbers: 11.10. Ef, 11.15.2q, 14.20.Gk, 13.75.Gx For decades the most commonly used propagator for spin-3/2 particles (e.g., the N and ∆ resonances) in particle and nuclear physics is the Rarita-Schwinger (RS) one [1], although it is also well known that the RS propagator has an intrinsic and long-standing problem [2,3]; it contains the unphysical extra degrees of freedom (DOF) or lower spin background. To be more precise, let us begin with the RS field that is formed by the tensor product of a vector and a Dirac field represented by (1/2, 1/2) and (1/2, 0) ⊕ (0, 1/2), respectively. This tensor productwhich shows that the RS field consists of two fields; the (1, 1/2) ⊕ (1/2, 1) and the Dirac field. The orthogonality relation can be used to eliminate the Dirac field. The (1, 1/2)⊕(1/2, 1) is, however, still not free from the Dirac background. So far, the popular choice for the interaction Lagrangian is given, e.g., in Eq. (16) of Ref.[5], which contains the so-called off-shell parameter. This parameter is required to maintain the invariance of the RS Lagrangian under point transformations [6]. In the phenomenological study of nuclear physics, however, the physical meaning of the off-shell parameter raised a serious problem, i.e., the coupling constants could heavily depend on the off-shell parameter [8] and the ∆ contribution for the Compton amplitude is obscured by this parameter [7]. There is also some infamous fundamental problem regarding the interaction with the electromagnetic field, i.e., the Johnson-Sudarshan [9] and Velo-Zwanziger [10] problems. The origin of these problems comes from the unphysical degree of freedom that arises in the interaction for whatever choice we make for the off-shell parameter.Furthermore, it is shown in Ref.[5] that this interaction does not posses any local symmetry of RS field and, as a consequence, it violates the constraints for reducing the number of independent components of the field to the correct value and involves the unphysical lower-spin DOF. The pathologies of this interaction can be removed by introducing the gauge-invariant (GI) or consistent interaction to decouple the unphysical spin-1/2 background from the ∆-exchanges amplitude [5].Nevertheless, for the practical use of spin-3/2 propagators and couplin...

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Higher-spin particles at high-energy colliders

Criado

Djouadi

Koivunen

et al. 2021

J. High Energ. Phys.

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Using an effective field theory approach for higher-spin fields, we derive the interactions of colour singlet and electrically neutral particles with a spin higher than unity, concentrating on the spin-3/2, spin-2, spin-5/2 and spin-3 cases. We compute the decay rates and production cross sections in the main channels for spin-3/2 and spin-2 states at both electron-positron and hadron colliders, and identify the most promising novel experimental signatures for discovering such particles at the LHC. The discussion is qualitatively extended to the spin-5/2 and spin-3 cases. Higher-spin particles exhibit a rich phenomenology and have signatures that often resemble the ones of supersymmetric and extra-dimensional theories. To enable further studies of higher-spin particles at collider and beyond, we collect the relevant Feynman rules and other technical details.

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Bosonic and fermionic Weinberg-Joos (j,0) ⊕ (0,j) states of arbitrary spins as Lorentz tensors or tensor-spinors and second-order theory

Cited by 19 publications

References 30 publications

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

Massless Rarita–Schwinger field from a divergenceless antisymmetric tensor-spinor of pure spin-3/2

Pure spin-3/2 propagator for use in particle and nuclear physics

Higher-spin particles at high-energy colliders

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