Solitons in classical field theories correspond to states quantum theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads infrared divergences, which generally regularized via wave packets or by compactification. However, some applications both possibilities undesirable. In present note, we introduce a finite inner product on translation-invari...

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of product, first show that each group is a torsion-free normed group. We give examples such and describe norms induced by products. Among other results, Hilbert groups, midconvex orthogonal subgroups are presented, Riesz representation theorem divisible proved.

We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using Donaldson’s quantization link between the infinite and finite dimensional G.I.T quotients that describe moduli spaces of varieties, we define a natural sequence of Kähler metrics. We prove that the sequence converges to the Weil-Petersson metric. ...

We introduce a coarse combinatorial description of the Weil-Petersson distance dWP(X, Y ) between two finite area hyperbolic Riemann surfaces X and Y . The combinatorics reveal a connection between Riemann surfaces and hyperbolic 3-manifolds conjectured by Thurston: the volume of the convex core of the quasi-Fuchsian manifold Q(X, Y ) with X and Y in its boundary is comparable to the Weil-Peter...