Vol. 26 (1988) REPORTS ON MATHEMATICAL PHYSICS No. 3 PROBABILISTIC FINSLER GEOMETRY AND THE 4n-PERIODICITY FACTOR OF A SPINOR WAVE FUNCTION SISIR ROY Indian Statistical Institute, Calcutta 700035, India zyxwvutsrqponmlkjihgfedc (Received November Il. 1987) The possibility of breaking W(2) symmetry due to the fluctuation of the Finslerian metric has been considered. The experimental indication with neutron interferometry is not conclusive regarding any deviation from 4n-symmetry of the spinor wave function of the realizing the Finslerian structure of the space-time metric in nature. Introduction It is well known that a 27c-rotation produces a phase factor of - 1 of the $-function in quantum mechanics. But it is not an observable quantity since the expectation values are quadric in the wave function. Aharanov and Susskind [l] and independently Bernstein [2], predicted that the 4n-factor may be observed in certain experiments. More and more suggestions were made by different workers [3] with neutron and electron interferometers. Rauch et. al. [4] first verified the 4x-periodicity of the spinor wave function using the perfect crystal neutron interferometer. Successive measurements were carried out by other groups of workers [S]. Subsequently a precise measurement of this 4n-symmetry effect was performed [6] which yields, after corrections for the new values of the fundamental constants, a periodicity factor of 01 = 715.87 f 3.8 deg which includes the 729deg within its 2a-error limits. The recent generalization of quantum mechanics [7] considering the violation of Pauli principle and SU (2) within the range of strong interaction predicts a deviation of the 4x-periodicity. The theory predicts a mutation of the spin value to S, = t+s. No estimates of E are available at present from the theory. The recent developments of probabilistic metric spaces in the micro-level raise a possibility of estimating this parameter E( - 3 x 10e3) which agrees well with the results obtained from recent measurements by neutron interferometry. However this might indicate an anoma- lous value of the magnetic moment of the neutron within the nucleus. It would be thus desirable to perform more refined experiments of the magnetic moment of thr neutron under strong interaction. [361]’