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arXiv · 1401.6526

Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators

Raoelina Andriambololona·Ravo Tokiniaina Ranaivoson·Rakotoson Hanitriarivo·Victor Harison
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Abstract

We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators, we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

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Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Rakotoson Hanitriarivo, Victor Harison. 2014-02-25. Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators. https://arxiv.org/abs/1401.6526

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