Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans’ theory and show that it yields two field equations. The second field equation is algebraic in the torsion...

The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed point of the effective scalar theory. ⋆ On leave from Pedagogical Institute, 634041 Tomsk, Russia In a recent paper [1] the trace anomaly induced dynamics of...

In this paper we study M-theory compactifications on seven-dimensional manifolds with SU(3) structure. As such manifolds naturally pick up a specific direction and the resulting effective theory can be recast into a form which is very similar to type IIA compactifications to four dimensions. We derive the gravitino mass matrix in four dimensions and show that for different internal manifolds (t...

Hydrogen bonding of DPPE with water that surrounded of membrane, plays an important role in permeability ofmembrane that we were presented this matter with analysis of bond angles and torsion angles before and after ofadded water molecules.Interaction with water molecules causes some changes in the geometry of DPPE which were explained bythe contribution of zwitterionic form of DPPE molecule, a...

Abstract We generalize Einstein’s General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed the Cambridge group. GTG a “spin-torsion” theory, according which, gravitational effects are described pair of gauge fields defined over flat Minkowski background spacetime. The con...

We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems. We shall present here some conjectures, problems and open questions related to flat manifolds. By flat manifold we understand a compact closed (without boundary) Riemanni...

It is shown in this paper that the topological phenomenon ”zero in the continuous spectrum”, discovered by S.P.Novikov and M.A.Shubin, can be explained in terms of a homology theory on the category of finite polyhedra with values in certain abelian category. This approach implies homotopy invariance of the Novikov-Shubin invariants. Its main advantage is that it allows to use the standard homol...

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.