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arXiv · 0710.1423

Duffin-Kemmer-Petiau formalism reexamined: non-relativistic approximation for spin 0 and spin 1 particles in a Riemannian space-time

A. A. Bogush·V. V. Kisel·N. G. Tokarevskaya·V. M. Red'kov
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Abstract

It is shown that the generally covariant Duffin-Kemmer-Petiau equation, formulated in the frame of the Tetrode-Weyl-Fock-Ivanenko tetrad formalism, allows for a non-relativistic approximation if the metric tensor is of a special form. The Pauli equation for a vector particle involves the Riemann curvature tensor explicitly. In analogous way, the procedure of the non-relativistic approximation in the theory of scalar particle, charged and neutral, is investigated in the background of Riemannian space-time. A generalized covariant Schrodinger equation is derived when taking into account non-minimal interaction term through scalar curvature R(x), it substantially differs from the conventional generally covariant Schrodinger equation produced when R(x)=0. It is demonstrated that the the non-relativistic wave function is always complex-valued irrespective of the type of relativistic scalar particle, charged or neutral, taken initially. The theory of vector particle proves the same property: even if the wave function of the relativistic particle of spin 1 is taken real,the corresponding wave function in the non-relativistic approximation is complex-valued.

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A. A. Bogush, V. V. Kisel, N. G. Tokarevskaya, V. M. Red'kov. 2007-10-07. Duffin-Kemmer-Petiau formalism reexamined: non-relativistic approximation for spin 0 and spin 1 particles in a Riemannian space-time. https://arxiv.org/abs/0710.1423

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