2015
DOI: 10.1140/epja/i2015-15035-x
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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

Abstract: 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,… Show more

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Cited by 19 publications
(33 citation statements)
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References 30 publications
(88 reference statements)
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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%
“…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%
“…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.…”
mentioning
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.…”
mentioning
confidence: 99%
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