Wave Equations on a Hyperplane

Hammer, C. L.; McDonald, S. C.; Pursey, D. L.

doi:10.1103/physrev.171.1349

Cited by 29 publications

(15 citation statements)

References 15 publications

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“…( 25) was firstly considered in [21] following a different approach, including electromagnetic interactions at the classical level. Closely related work was also done in [22], [23]. The present approach, based on the parity and Poincaré projections, permits us to identify all quantum numbers from first principles.…”

Section: B the Spin-one Parity Projectionmentioning

confidence: 98%

Spin one matter fields

Napsuciale,

Rodríguez,

Ferro-Hernández

et al. 2015

Preprint

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Spin-one matter fields are relevant both for the description of hadronic states and as potential extensions of the Standard Model. In this work we present a formalism for the description of massive spin-one fields transforming in the (1, 0) ⊕ (0, 1) representation of the Lorentz group, based on the covariant projection onto parity eigenspaces and Poincaré orbits. The formalism yields a constrained dynamics. We solve the constraints and perform the canonical quantization accordingly. This formulation uses the recent construction of a parity-based covariant basis for matrix operators acting on the (j, 0) ⊕ (0, j) representations. The algebraic properties of the covariant basis play an important role in solving the constraints and allowing the canonical quantization of the theory. We study the chiral structure of the theory and conclude that it is not chirally symmetric in the massless limit, hence it is not possible to have chiral gauge interactions. However, spin-one matter fields can have vector gauge interactions. Also, the dimension of the field makes self-interactions naively renormalizable. Using the covariant basis, we classify all possible self-interaction terms.

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Section: B the Spin-one Parity Projectionmentioning

confidence: 98%

Spin one matter fields

Napsuciale,

Rodríguez,

Ferro-Hernández

et al. 2015

Preprint

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“…Similar arguments apply equally well to the arbitrary spin equations derived in Section 2 and to the arbitrary spin equation (2) of Joos and Weinberg considered in the Introduction. Hammer et al (1968) have shown that the hyperplane formalism of Fleming (1966) can be used to ensure that the wavefunction components of equation (2) always obey the Klein-Gordon equation. We considered an alternative procedure in Section 2.…”

Section: Pmentioning

confidence: 99%

Component Minimization of the Bargmann?Wigner Wavefunction

Jeffery¹

1978

Aust. J. Phys.

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The Bargmann-Wigner equations are used to derive relativistic field equations with only 2(2j+ 1) components of the original wavefunction. The other components of the Bargmann-Wigner wavefunction are superfluous and can be defined in terms of the 2(2j+ 1) components. The results are compared with various 2(2j+ 1) theories in the literature. Sylvester's theorem and some properties of induced matrices give simple relationships between the operator matrices of the field equations and the arbitrary spin operator matrices.

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“…In refs. [9,17,4,18,19] the Feynman diagram technique was discussed in the abovementioned six-component formalism for particles of spin j = 1. The following Lagrangian: 5,6…”

mentioning

confidence: 99%

“…The following expression has been obtained for the interaction vertex of the particle with a photon described by the vector potential, ref. [17,18]:…”

mentioning

confidence: 99%

Interactions of aj=1 boson in the 2(2j+1) component theory

Dvoeglazov

1996

Int J Theor Phys

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The amplitudes for boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the used model is the Weinberg's 2(2j + 1) component formalism for describing a particle of spin j, recently developed substantially. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the ground of the hamiltonian formulation of quantum field theory on the mass hyperboloid, p 2 0 − p 2 = M 2 , proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T matrices for the fermion and the boson cases. However, certain differences are found. Possible physical applications are discussed.

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Wave Equations on a Hyperplane

Cited by 29 publications

References 15 publications

Spin one matter fields

Spin one matter fields

Component Minimization of the Bargmann?Wigner Wavefunction

Interactions of aj=1 boson in the 2(2j+1) component theory

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