Quantum Effects of a Vortex Gravitational Field and the Torsion of Spacetime

Possible quantum effects, induced by the torsion of spacetime described by its pseudotrace Q⌣i=16εiklmQklm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overset{\smile }{Q}}^i=\frac{1}{6}{\upvarepsilon}^{iklm}{Q}_{klm} $$\end{document}, and by a vortex gravitational field described by its angular velocity ωi=12εiklmeakelma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\upomega}^i=\frac{1}{2}{\upvarepsilon}^{iklm}{e}_{ak}{e}_{lm}^a $$\end{document} of rotation of the tetrad field eakxi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {e}_a^k\left({x}^i\right) $$\end{document}, are considered. Toward this end, the vacuum averages <0Tki0>\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ <0\left|{T}_k^i\right|0> $$\end{document} of the energy-momentum tensor Tki\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {T}_k^i $$\end{document} of the quantized scalar field are calculated. A thorough-going analogy between physical effects induced by these two physical objects is revealed both on the classical and on the quantum level.