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Adjunctation and Scalar Product in the Dirac Equation - I

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Abstract

The Bargmann-Pauli adjunctator (hermitiser) of \(\mathcal {C}{l}_{_{1,3}}(C)\) is derived in a representation independent way, circumventing the early derivations (Pauli, Ann. inst. Henri Poincaré 6, 109 and 121 1936) using representation-dependent arguments. Relations for the adjunctator’s transformation with the scalar product and space generator set are given. The S U(2) adjunctator is shown to determine the \(\mathcal {C}{l}_{_{1,3}}(C)\) adjunctator. Part-II of the paper will approach the problem of the two scalar products used in Dirac theory - an unphysical situation of “piece-wise physics” with erroneous results. The adequate usage of scalar product - via calibration - will be presented, in particular under boosts, yielding the known covariant transformations of physical quantities.

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Notes

  1. 1 Further more, while for real-space G Minkowski is unique, for quantum-space # #π# #=γ 0 is not unique in having this (convenient, but non-physical) property, # #π# #=γ 0(a+b γ 5) satisfying equally well.

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Acknowledgments

This work was supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project no. PN-II-ID-PCE-2011-3-0323.

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  1. Institute for Physics and Nuclear Engineering, Str. Reactorului no.30, P.O.BOX MG-6, Bucharest, Magurele, Romania

    M. Dima

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Dima, M. Adjunctation and Scalar Product in the Dirac Equation - I. Int J Theor Phys 55, 949–958 (2016). https://doi.org/10.1007/s10773-015-2739-3

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