Wave equation for a magnetic monopole

Lochak, Georges

doi:10.1007/bf00670815

Cited by 52 publications

(50 citation statements)

References 21 publications

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“…A physical interpretation of the associated effective functional energy equation (21) of [6] can be achieved by considering the classical limit of this equation. In this classical limit the system is described by its classical equations of motion.…”

Section: Effective Canonical Equations Of Motionmentioning

confidence: 99%

“…In this classical limit the system is described by its classical equations of motion. These equations of motion can be exactly derived from equation (21) of [6], if correlations in the matrix elements are suppressed. For details of the corresponding deduction we refer to [13], section 7.5 for instance.…”

Section: Effective Canonical Equations Of Motionmentioning

confidence: 99%

“…In its magnetic part this equation is a generalization of Lochak's massless magnetic monopol equation (1.9) in [21], to magnetic electroweak interactions, and in addition this equation contains the full "electric" and "magnetic" electroweak interaction with corresponding massive fermions. For the sake of brevity the effect of symmetry breaking on the fermion masses is not treated in detail.…”

Section: Modification Of β β β -Decay Processesmentioning

confidence: 99%

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Change of Electroweak Nuclear Reaction Rates by CP- and Isospin Symmetry Breaking – A Model Calculation

Stumpf

2006

Zeitschrift Für Naturforschung A

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Based on the assumption that electroweak bosons, leptons and quarks possess a substructure of elementary fermionic constituents, in previous papers the effect of CP-symmetry breaking on the effective dynamics of these particles was calculated. Motivated by the phenomenological procedure in this paper, isospin symmetry breaking will be added and the physical consequences of these calculations will be discussed. The dynamical law of the fermionic constituents is given by a relativistically invariant nonlinear spinor field equation with local interaction, canonical quantization, selfregularization and probability interpretation. The corresponding effective dynamics is derived by algebraic weak mapping theorems. In contrast to the commonly applied modifications of the quark mass matrices, CP-symmetry breaking is introduced into this algebraic formalism by an inequivalent vacuum with respect to the CP-invariant case, represented by a modified spinor field propagator. This leads to an extension of the standard model as effective theory which contains besides the "electric" electroweak bosons additional "magnetic" electroweak bosons and corresponding interactions. If furthermore the isospin invariance of the propagator is broken too, it will be demonstrated in detail that in combination with CP-symmetry breaking this induces a considerable modification of electroweak nuclear reaction rates.

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Section: Effective Canonical Equations Of Motionmentioning

confidence: 99%

Section: Effective Canonical Equations Of Motionmentioning

confidence: 99%

Section: Modification Of β β β -Decay Processesmentioning

confidence: 99%

See 1 more Smart Citation

Change of Electroweak Nuclear Reaction Rates by CP- and Isospin Symmetry Breaking – A Model Calculation

Stumpf

2006

Zeitschrift Für Naturforschung A

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“…We remark that (5.21) has been called the Hertz theorem in [32,37] and it has been used there and also in [8,9,10,16,20,31,33] in order to find nontrivial superluminal solutions of the free Maxwell equation.…”

Section: Hertz Theorem the Hertz Potential Satisfiesmentioning

confidence: 99%

“…Under this condition, (6.27) becomes These results show that when a Dirac-Hestenes spinor field associated with the first of the Seiberg-Witten equations is in an eigenstate of the parity operator, that spinor field describes a pair of particles with opposite charges. We interpret these particles (following Lochak [16] who suggested that an equation equivalent to (8.10) describes massless monopoles of opposite charges) as being massless monopoles in auto-interaction. Observe that our proposed interaction is also consistent with the third of Seiberg-Witten equations, for F = dA implying a null magnetic current.…”

Section: Derivation Of Seiberg-witten Equationsmentioning

confidence: 99%

The relation between Maxwell, Dirac, and the Seiberg‐Witten equations

Rodrigues

2003

International Journal of Mathematics and Mathematical Sciences

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We discuss unsuspected relations between Maxwell, Dirac, and the Seiberg-Witten equations. First, we present the Maxwell-Dirac equivalence (MDE) of the first kind. Crucial to that proposed equivalence is the possibility of solving for ψ (a representative on a given spinorial frame of a Dirac-Hestenes spinor field) the equation F = ψγ 21ψ , where F is a given electromagnetic field. Such task is presented and it permits to clarify some objections to the MDE which claim that no MDE may exist because F has six (real) degrees of freedom and ψ has eight (real) degrees of freedom. Also, we review the generalized Maxwell equation describing charges and monopoles. The enterprise is worth, even if there is no evidence until now for magnetic monopoles, because there are at least two faithful field equations that have the form of the generalized Maxwell equations. One is the generalized Hertz potential field equation (which we discuss in detail) associated with Maxwell theory and the other is a (nonlinear) equation (of the generalized Maxwell type) satisfied by the 2-form field part of a Dirac-Hestenes spinor field that solves the Dirac-Hestenes equation for a free electron. This is a new result which can also be called MDE of the second kind. Finally, we use the MDE of the first kind together with a reasonable hypothesis to give a derivation of the famous Seiberg-Witten equations on Minkowski spacetime. A physical interpretation for those equations is proposed.2000 Mathematics Subject Classification: 81Q05, 81R25, 15A66.

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Maxwell, Dirac and Seiberg-Witten Equations

Rodrigues

Oliveira

2016

The Many Faces of Maxwell, Dirac and Einstein Equations

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Wave equation for a magnetic monopole

Cited by 52 publications

References 21 publications

Change of Electroweak Nuclear Reaction Rates by CP- and Isospin Symmetry Breaking – A Model Calculation

Change of Electroweak Nuclear Reaction Rates by CP- and Isospin Symmetry Breaking – A Model Calculation

The relation between Maxwell, Dirac, and the Seiberg‐Witten equations

Maxwell, Dirac and Seiberg-Witten Equations

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