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New Trends in Mathematical and Theoretical Physics
October 7, 2016 12:00–12:30, Moscow, MIAN, Gubkina, 8

On the one-particle formulation of the Dirac theory

Nikolay Chuprikov

Tomsk State Pedagogical University
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Nikolay Chuprikov
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Abstract: Dirac's theory is presented as a logically consistent four-component quantum theory of a relativistic particle with the half-integer spin. In this approach the complete system of independent solutions to the problem for a free Dirac particle with a definite energy and momentum, collinear to a given direction, contains four solutions for each sign of energy, rather than two, as in the standard approach. As was shown, solving the Dirac equation for a particle with a definite energy is reduced either to solving the generalized Pauli equation for a “heavy” quasiparticle or to solving the generalized Pauli equation for a “light” quasiparticle; the effective mass of each quasiparticle carriers information about the symmetry of the four-dimensional space-time. But Dirac’s theory is irreducible to the two-component Pauli theory even in the non-relativistic limit. Unlike the latter the former describes a particle with two internal degrees of freedom, rather than one. The second internal degree of freedom of the Dirac particles is associated with the intrinsic parity, with the (conditional) positive intrinsic parity being associated with the “heavy” quasiparticle and (conditional) negative intrinsic parity being associated with the “light” quasiparticle. “Physical states” of the Dirac particle always represent mixtures of states with positive and negative internal parities. For a particle with a definite energy and momentum the ratios of the effective masses to their sum give the probabilities of finding the Dirac particle in the corresponding subensembles of quasiparticles. The “formal states” of the Dirac particle with a negative energy should be considered as “physical states” of its antiparticle with a positive energy: no superposition of states of the Dirac particle with different signs of energy is allowed. The space of states with positive energies is closed with respect to the action of even and odd operators.

Language: English

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