Multy-Dimensional Theory of Gravity-Electro Interactions, Time Machine and Foliations

Guts, Alexander K.

American Physical Society, APS/AAPT Joint Meeting, May 2-5, 1996, abstract #J15.02

The space-time V^4 can be considered as a leaf of foliation \cal F of codimision q, q>= 1 in Lorentzian manifold V^{4+q}. In some cases the leaf V^4 infinitely winds round (wraps) itself and so the Past or Future lies in any small neighbourhood (in topology of V^{4+q}) of the Present. This leaf is called spring leaf. We can transfer to the such near Past throught the 4-dimensional wormhole along timelike geodesic in V^{4+q} (A.K.Guts, Izvestija VUZov. Fizika (Russian), N 2 (1996) ).

How will it understand that our space-time is the spring leaf? The 6-dimensional theory of gravity-electro-weak interactions (Ju.S.Vladimirov, Dimension of physical space-time and union of interactions. -- Moscow state univ., 1987. ) connects the vector fields A_\mu and Z_\mu (\mu=0,1,2,3) with differential 1-forms \lambda=\lambda_Adx^A and \sigma=\sigma_Adx^A (A=0,1,2,3,5,6), where G_AB=g_AB-\lambda_A\lambda_B -\sigma_A\sigma_B is the metric of V^6 and g_AB is metric of V^4. The 1-forms \lambda, \sigma define the characteristic classes of foliation \cal F.

The calculation of these cohomological classes gives the answer to the question. For example under q=1 there exists only one such class GV(\cal F) that is called the Godbillon-Vey class, and if GV(\cal F)neq 0 then \cal F has a spring leaf. Hence the investigation of electro-weak interactions allows to solve some principal questions that concerns to Time machine.