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**Quantum features of non-symmetric geometries.**
*(English)*
Zbl 0943.83044

Summary: Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization schemes, paths in such geometries are naturally quantized. Two different non-symmetric geometries are examined for these features. It is proved that, whatever the non-symmetric geometry is, we always get the same quantum features. It is shown that these features appear only in the pure torsion term (the anti-symmetric part of the affine connection) of the path equations. The vanishing of the torsion leads to the disappearance of these features, regardless of the symmetric part of the connection. It is suggested that, in order to be consistent with the results of experiments and observations, torsion term in path equations should be parametrized using an appropriate parameter.

### MSC:

83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |

81T20 | Quantum field theory on curved space or space-time backgrounds |

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\textit{M. I. Wanas} and \textit{M. E. Kahil}, Gen. Relativ. Gravitation 31, No. 12, 1921--1929 (1999; Zbl 0943.83044)

### References:

[1] | Robertson, H. P. (1932) · Zbl 0005.11902 |

[2] | Einstein, A. (1955). The Meaning of Relativity (Princeton University Press, Princeton NJ); Moffat, J. W · Zbl 0067.20404 |

[3] | Wanas, M. I., Melek, M., and Kahil, M. E. (1995 · Zbl 0846.53069 |

[4] | Bazanski, S. L. (1977). Ann |

[5] | Isham, C. J. (1997). In Proc. General Relativity and Gravitation 14, M. Francaviglia, ed. (World Scientific, Singapore). |

[6] | Wanas, M. I. (1998 · Zbl 0947.83042 |

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