On the Spin of Gravitational Bosons

Ahluwalia, Dharam Vir; Dadhich, Naresh; Kirchbach, Mariana

doi:10.1142/s0218271802003031

Cited by 18 publications

(36 citation statements)

References 38 publications

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“…The (1, 0)⊕(0, 1) sector is well known and has been frequently elaborated in the literature, listed among others in [23], [16]. We here present it in the momentum space, and denote it by, B…”

Section: The Anti-symmetric Lorentz Tensor Spinor Of Second Rankmentioning

confidence: 99%

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

2015

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We propose a general method for the description of arbitrary single spin-j states transforming according to (j, 0) ⊕ (0, j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensorspinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher ∂ 2j order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j, 0)⊕(0, j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz-and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentztensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2, 0)⊕(0, 3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, Ψ [µν] . Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2, 0) ⊕ (0, 3/2) as part of Ψ [µν] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents 1 itself very computer friendly with respect to the symbolic software FeynCalc.

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Section: The Anti-symmetric Lorentz Tensor Spinor Of Second Rankmentioning

confidence: 99%

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

2015

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“…[35,36,37], have exposed the fact that the arguments advocated in Refs. [33,34] clearly assuming that the underlying spacetime be classical (or at least commutative). The studies reported in Refs.…”

Section: Main Features Of Dsr2mentioning

confidence: 99%

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

Amelino‐Camelia

Benedetti²,

D’Andrea³

et al. 2003

Class. Quantum Grav.

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We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energymomentum-conservation rules in these theories with two relativistic invariants.

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“…In the current section we consider massless four-vectors as direct products of Weyl spinors and co-spinors, an approach inspired by [11], [12] where the massive four-vectors have been described in terms of direct products of massive left-and right-handed spinors. For that purpose we begin by calculating χ⊗ τ , ρ ⊗ φ, χ⊗ φ and ρ ⊗ τ .…”

Section: Massless (1/2 1/2) Polarization Vectorsmentioning

confidence: 99%

“…Put another way, this means that (−iA 2 ) = e z transforms according to a trivial representation. In this way the massless (1/2, 1/2) representation of the Lorentz group, in contrast to the massive one [11], [12], is not irreducible but splits into a trivial representation, i.e. an so(1, 2) singlet, defined by the constant vector, (−iA 2 ) = e z , coinciding with the unit vector of the z axis, on one side, and an so(1, 2) triplet constituted by the two vectors, (−iA 1 ) = ǫ 1,1 , and (−iA 3 ) = ǫ 1,−1 , of negative norms, and time-like vector (−iA 4 ) = ǫ 1,0 ≡ n of a positive norm, on the other.…”

Section: Classification Of the Massless Four-vectors By The Casimir Imentioning

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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On the Spin of Gravitational Bosons

Cited by 18 publications

References 38 publications

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

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

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

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

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