Component Minimization of the Bargmann?Wigner Wavefunction

Jeffery, EA

doi:10.1071/ph780137

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…As such, we cannot hope to retain its algebraic structure and describe a system with arbitrary spin. A standard approach to overcome this problem is to construct a tensor power algebra Cl(E, δ) ⊗k ; this algebra contains a Clifford substructure yet contains subalgebras with the structure of arbitrary spin systems [28] for large enough k. Indeed, subspaces of tensor products of this algebra also underpin the definition of many classic higher spin models [4,18,19].…”

Section: Limitations Of Clifford Algebra-based Approachmentioning

confidence: 99%

A Relationship Between Spin and Geometry

Bradshaw

2024

Adv. Appl. Clifford Algebras

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In physics, spin is often seen exclusively through the lens of its phenomenological character: as an intrinsic form of angular momentum. However, there is mounting evidence that spin fundamentally originates as a quality of geometry, not of dynamics, and recent work further suggests that the structure of non-relativistic Euclidean three-space is sufficient to define it. In this paper, we directly explicate this fundamentally non-relativistic, geometric nature of spin by constructing non-commutative algebras of position operators which subsume the structure of an arbitrary spin system. These “Spin-s Position Algebras” are defined by elementary means and from the properties of Euclidean three-space alone, and constitute a fundamentally new model for quantum mechanical systems with non-zero spin, within which neither position and spin degrees of freedom, nor position degrees of freedom within themselves, commute. This reveals that the observables of a system with spin can be described completely geometrically as tensors of oriented planar elements, and that the presence of non-zero spin in a system naturally generates a non-commutative geometry within it. We will also discuss the potential for the Spin-s Position Algebras to form the foundation for a generalisation to arbitrary spin of the Clifford and Duffin–Kemmer–Petiau algebras.

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Section: Limitations Of Clifford Algebra-based Approachmentioning

confidence: 99%

A Relationship Between Spin and Geometry

Bradshaw

2024

Adv. Appl. Clifford Algebras

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“…that are essentially the Bargmann-Wigner equations. In general there is no distinguished way to select one equation, and the set of r equations corresponds to no obvious, natural Lagrangian formulation [1,16,26,20,24,27]. Alternatively one may consider a single equation of order r , namely…”

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confidence: 99%

A first-order Lagrangian theory of fields with arbitrary spin

Canarutto¹

2018

Int. J. Geom. Methods Mod. Phys.

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The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic 'building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved spacetime. In particular, one recovers the Bargmann-Wigner equations and the 2(2j + 1)-dimensional representation of the angular-momentum algebra needed for the Joos-Weinberg equations. Looking for a first-order Lagrangian field theory we argue, through considerations related to the 2-spinor description of the Dirac map, that the needed bundle must be a fibered direct sum of a symmetric 'main sector'-carrying an irreducible representation of the angularmomentum algebra-and an induced sequence of 'ghost sectors'. Then one indeed gets a Lagrangian field theory that, at least formally, can be expressed in a way similar to the Dirac theory. In flat spacetime one gets plane-wave solutions that are characterised by their values in the main sector. Besides symmetric spinors, the above procedures can be adapted to anti-symmetric spinors and to Hermitian spinors (the latter describing integer-spin fields). Through natural decompositions, the case of a spin-2 field describing a possible deformation of the spacetime metric can be treated in terms of the previous results.MSC 2010: 81R20, 81R25.

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“…Since then, various theorists did further research in relativistic Hamiltonians for particles with higher-spins [13][14][15]. Although the Dirac equation is considered as the generally accepted relativistic wave interpretation for relativistic particles, there were few other interpretations to the Dirac equation without using spinors.…”

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confidence: 99%

On the Complementary Wave Interpretation of the Dirac Equation

Bulathsinghala

Gamalath

2013

ILCPA

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The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.

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Component Minimization of the Bargmann?Wigner Wavefunction

Cited by 5 publications

References 8 publications

A Relationship Between Spin and Geometry

A Relationship Between Spin and Geometry

A first-order Lagrangian theory of fields with arbitrary spin

On the Complementary Wave Interpretation of the Dirac Equation

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