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• W2069415415 abstract "It is supposed that there exists a system O′ (intrinsic system) in which the field equation for a spin ½ representation has the simple form γ µ ∂Ψ′/∂ϰ μ′ =0. This system is related to the physical system (in which all measurements are performed) by an affine connection which is induced by a certain group of local transformations. The investigation given here deals with the group of local four-dimensional complex orthogonal transformations. Subjecting ψ' to such a transformation Ω one gets with ψ' (x′) = Ω (x) ψ (x) the following equation γ λ ∂Ψ/∂x λ +γ λ Ω -1 ∂Ω/∂x λ ψ=0. The interaction term splits up into a vector and a pseudovector part: γ λ Ω -1 ∂Ω/∂x λ ≡ γ λ V λ +γ λ γ 5 Ρ λ . The special cases of real local orthogonal (LORENTZ-) transformations (ξ λμ = - ξ μλ ; ξ kl real, ξ 4l imaginary; ψ → χ) and special complex local orthogonal transformations (η λμ =- η μλ ; η kl imaginary, η 4l real; ψ → φ) are first separately considered. It is required that V λ and P λ are to be built up from the fundamental covariants of the field. In order that certain conservation laws hold at least approximately, the following assumptions are made: Im{V k }=±k 2 ɸ̅γ k φ, Re {V 4 }=±k 2 γ 4 φ, Im {P k } = ± l 2 χ̅ γ k γ 5 χ, Re {P 4 }= ±l 2 χ̅γ 4 γ 5 χ together with the symmetry conditions for the transformation parameters, ξ λ[μυ] ≡ 0, η 〈λμ,υ〉 ≡ 0, which can be fulfilled by setting, for example, ξ λμ,υ = π [λ π μ,υ] ,η λμ = ϑ [λ,μ] . The remaining parts of V λ and Ρ λ , which are determined by these relations, are of higher order and can be assumed to describe weaker interactions. Neglecting these terms one obtains the following set of equations: (a) γ λ ∂χ/∂x λ ±k 2 γ λ (ɸ̅γ λ φ) χ±l 2 γ λ γ 5 (χ̅γ λ γ 5 χ) χ≈0 (b) γ λ ∂χ/∂x λ ±k 2 γ λ (ɸ̅γ λ φ) φ±l 2 γ λ γ 5 (χ̅γ λ γ 5 χ) φ≈0 Since the pseudovector coupling possesses a greater symmetry, it is assumed that χ represents the baryon and φ the lepton states. Within the approximation, which holds with (a) and (b), it follows the conservation of χ̅γ λ χand ɸ̅γ λ φ resp. (conservation of electric charge) and χ̅γ λ γ 5 χ and ɸ̅ γ· λ γ 5 φ resp. (conservation of baryonic and leptonic charge resp.). These conservation laws are exact only if the mentioned terms of higher order are neglected; this is equivalent to a strict “local” conservation as can be shown. As to the isospin it is proposed to replace one of its components by a bounded state, i. e. a mixture of χ- and φ-states which would lead in the case of the neutron for example to the components of the /?β-decay. Due to the relations ± k 2 ɸ̅γ λ φ = ¼η λρ ,ρ +O(η 2 ) and η λu = ϑ [λμ] , and in agreement with the reality conditions, it is possible to connect the parameters ϑ λ with the electromagnetic field A λ by setting ϑ λ = 8 iA λ . Taking into consideration terms of higher order this would lead to a type of nonlinear electrodynamics." @default.
• W2069415415 created "2016-06-24" @default.
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• W2069415415 date "1965-05-01" @default.
• W2069415415 modified "2023-10-04" @default.
• W2069415415 title "On the Rôle of the Group O4 of Local Complex Orthogonal Transformations in a Nonlinear Theory of Elementary Particles" @default.
• W2069415415 doi "https://doi.org/10.1515/zna-1965-0502" @default.
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