Seminar

1. Saha Bijan

   Spinor field in cosmology with Lyra's geometry

   Abstract:
   

   In this talk, within the scope of a Bianchi type-I anisotropic cosmological model with Lyra’s geometry, we study the role of a nonlinear spinor field in the evolution of the Universe. Earlier we have considered the nonlinear spinor field in Bianchi type-I geometry and found that the presence of nontrivial non-diagonal components of the energy momentum tensor leads to either the elimination of spinor field nonlinearity and spinor mass or the space-time anisotropy. In the present talk, we will discuss the role of Lyra’s geometry and see whether it can remove these severe restrictions of space-time geometry or the spinor field itself. Since the spinor field is very sensitive to geometry, we hope that it can undergo some changes. Although the spinor affine connection and Einstein equations are changed, the final results remain almost the same, at least in this model.

2. Е.Е. Perepelkin (JINR), B.I. Sadovnikov (MSU), N.G. Inozemtseva (MTUCI), P.V. Afonin (MSU), R.V. Polyakova (JINR)

   Properties of the quasiprobability density functions of a quantum system with electromagnetic interaction

   Abstract:

   The paper considers the description of a quantum system with electromagnetic interaction within the quasiprobability density function apparatus. The properties of the Wigner function and the Weyl-Stratonovich function are compared on the three-dimensional exact solutions of the Schrödinger equation corresponding to the Ψ-model. As known, the Weyl-Stratonovich function, unlike the Wigner function, has gauge invariance.

   The average values of momenta and energies of the quantum system, which agree for both functions, are found explicitly. A significant difference between the Wigner function and the Weyl-Stratonovich function lies in the momentum probability density. It is shown that the Weyl-Stratonovich function is not positive for Gaussian wave functions. Wave functions (Ψ-model), for which the Weyl-Stratonovich function is positive, are found, which leads to an extension of Hudson’s theorem and its generalization to the three-dimensional case for the gauge-invariant Weyl-Stratonovich function.

Information on the seminar are available at Indico.