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Variational theory of an ideal spin liquid in the quadratic theory of gravitation in a Riemann-Cartan space

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Abstract

A variational theory of an ideal Weyssenhoff-Raabe spin liquid in a Riemann-Cartan space is constructed in the metric theory of gravitation (taking into account the quadratic invariants in the Lagrangian). The couplings which arise in the theory and are imposed on the dynamical variables are taken into account in the action integral with the help of the method of undetermined Lagrange multipliers. The canonical energy-momentum tensor of an ideal spin liquid arises in a natural manner as a source on the right side of the gravitational field equations.

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Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 10, pp. 101–105, October, 1989.

In conclusion I thank Professor V. N. Ponomarev and B. N. Frolov for their constant interest in this work and for a discussion of the results.

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Baburova, O.V. Variational theory of an ideal spin liquid in the quadratic theory of gravitation in a Riemann-Cartan space. Soviet Physics Journal 32, 849–853 (1989). https://doi.org/10.1007/BF00898321

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Keywords

  • Lagrange Multiplier
  • Field Equation
  • Gravitational Field
  • Dynamical Variable
  • Variational Theory