Physical Consequences of a Theory with Dynamical Volume Element
  We survey motivation, basic ideas and physical consequences of a theory where the underlying action involves terms both with the usual volume element $\sqrt{-g}d^{4}x$ and with the new one $\Phi d^{4}x={4!}d\varphi_{1}\wedge d\varphi_{2}\wedge d\varphi_{3}\wedge d\varphi_{4}$. The latter may be interpreted as the 4-form determined on the 4-D space-time manifold (not necessary Riemannian). Regarding the scalar fields $\varphi_{a} (a=1,...4)$ as new dynamical variables and proceeding in the first order formalism we realize the so-called Two Measures Theory which possesses a number of attractive features. We discuss new physical effects which arise from this theory and in particular strong gravity effect in high energy physics experiments. 
E. I. Guendelman and A. B. Kaganovich