Causality and theg-factor for a spin-one particle

Prabhakaran, J.; Seetharaman, M.

doi:10.1007/bf02735142

Cited by 8 publications

(6 citation statements)

References 10 publications

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“…In the case ρ = 0 and for positive parity our theory based on the off-shell projectors reproduces an equation proposed by Shay and Good in [11]. For arbitrary ρ this theory reproduces the Shay-Good equation with a magnetic-dipole term which has been shown in [21] to be classically causal only for ρ = 1/2. As for the tensor formalism, we show that the conformally invariant action used by Chizhov in Ref.…”

Section: Discussionsupporting

confidence: 78%

“…This formalism corresponds to an "anomalous" gyromagnetic factor of 1/2 (total gyromagnetic factor g = 1) of our theory based on the off-shell parity projection. In [25] it has been shown that at the classical level this theory is causal in agreement with results in [21].…”

supporting

confidence: 75%

“…( 104)). The classical causality properties of the Shay-Good equation when an "anomalous" magnetic-dipole term is included was studied in [21] which conclude that only in the case when the gyromagnetic factor take the value g = 1, i.e. when ρ = 1/2, the theory is causal.…”

Section: Mapping To the Antisymmetric Field And Comparison With Exist...mentioning

confidence: 99%

“…The off-shell formulation, with a vanishing "anomalous" magnetic moment, corresponds to a theory considered previously in [11] [15] in spinor language. This theory with a nonvanishing "anomalous" magnetic moment was analyzed in [21], where it is shown that the classical theory is causal only for a total gyromagnetic factor g = 1.…”

mentioning

confidence: 99%

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Parity-based formalism for high spin matter fields

Napsuciale,

Gómez-Ávila

2013

Preprint

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Using the recent parity-based construction of a covariant basis for operators acting on the (j, 0) ⊕ (0, j) representation of the Homogeneous Lorentz Group, we propose a formalism for the description of high spin matter fields, based on the projection over subspaces of well-defined parity. We identify two possibilities for the projection (on-shell and off-shell projection) which in general yield equivalent free theories but different interacting theories. For all j except for j = 1/2, we find that the projection does not completely fix the properties of the interacting theory. This freedom is related to the fact that the covariant form of parity can be written in terms of one of the symmetric traceless tensors in the covariant basis and in general allows for a free magnetic dipole term in the lagrangian. We gauge the theory and construct the charge conjugation operator showing that it commutes with parity for bosons, and anticommute in the case of fermions as expected. In the case of bosons, the parity invariant subspaces are also invariant under charge conjugation and time reversal and the formulation of a quantum field theory can be done using only these subspaces. As a first exhaustive example we work out the electrodynamics for j = 1 matter bosons, rewrite the theory in terms of an antisymmetric tensor field and compare our results with existing formalisms in the literature, either in tensor or "spinor" language. We find that there are three essentially different formalisms: i) formalisms equivalent to the on-shell parity projection, ii) formalisms equivalent to the off-shell parity projection and iii) the Poincaré projector formalism which describes a degenerate parity doublet. In particular, the tensor formalism used in chiral perturbation theory with resonances (RχP T ) is the same as a theory proposed by Shay and Good in "spinor" language and corresponds to our theory based on the off-shell parity projection. Also, a theory proposed by Joos and Weinberg in"spinor" basis is the same as the "antisymmetric tensor matter field" formalism used by Chizhov (in the massless case) and corresponds to our on-shell parity projection.Naive power counting admits anomalous magnetic-dipole terms and self-interactions at tree level. We perform a chiral decomposition of these theories and show that chiral symmetry can be realized linearly only for the theory based on the on-shell projection. Chiral symmetry forbids mass and anomalous magnetic dipole terms and in general admits six self-interaction terms. We conclude that this is the appropriate framework to attempt the incorporation of spin 1 matter bosons in chiral theories like the standard model.

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Section: Discussionsupporting

confidence: 78%

supporting

confidence: 75%

Section: Mapping To the Antisymmetric Field And Comparison With Exist...mentioning

confidence: 99%

mentioning

confidence: 99%

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Parity-based formalism for high spin matter fields

Napsuciale,

Gómez-Ávila

2013

Preprint

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“…As the nature (purely real or not) of the eigenvalue spectrum of S . n has an important bearing on the nature of energy eigenvalues of spin-1 Hamiltonians (see, for instance, Weaver's treatment (Weaver 1976) of the Sakata-Taketani (Taketani and Sakata 1940) Hamiltonian for spin-1 with a specific anomalous coupling with a constant magnetic field) and there exists a general connection between the possible occurrence of complex energy eigenvalues and the problem of acausality of propagation for spin-1 (see for instance, Krase er a1 1971, Goldman and Tsai 1971, Prabhakaran and Seetharaman 1973, Mathews 1974, it is pertinent to reinvestigate as to the exact nature of the eigenvalue spectrum of S . n for spin-1.…”

mentioning

confidence: 99%

On the Error of Averaging Symmetric Elliptic Systems

Pozhidaev¹,

Yurinskii²

1990

Math. USSR Izv.

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Exploiting the intimate connection of the problem of a charged spin-1 particle in a homogeneous magnetic field to that of a harmonic oscillator, we demonstrate explicitly that the eigenvalues of the matrix operator S . n for spin-1 and for a constant magnetic field are governed by a Hermitian matrix defined on the space of the particle number n and spin and are thus constrained to be real for any intensity of the external magnetic field H, thereby contradicting a recent affirmation of Weaver that for n = 0, complex eigenvalues are present for sufficiently intense magnetic fields. We also point out the errors that have crept into Weaver's analysis which have led to complex eigenvalues and as well to an excessive number of eigenvalues compared with that demanded by the spin degrees of freedom.

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