In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal this paper is to prove corresponding results geometric approach theory. We apply these formalism L-functionals.

The Milnor Problem (modified) in the theory of group growth asks whether any finite presented vanishing algebraic entropy has at most polynomial growth. We show that a positive answer to is equivalent Nilpotency Conjecture Riemannian geometry: given $n, d>0$, there exists constant $\epsilon(n,d)>0$ such if compact $n$-manifold $M$ satisfies Ricci curvature $\op{Ric}_M\ge -(n-1)$, diameter $d\ge...