Schwarzian functional integrals calculus

Chen Integrals , Generalized Loops and Loop Calculus

We use Chen iterated line integrals to construct a topological algebra Ap of separating functions on the Group of Loops LMp. Ap has an Hopf algebra structure which allows the construction of a group structure on its spectrum. We call this topological group, the group of generalized loops L̃Mp. Then we develope a Loop Calculus, based on the Endpoint and Area Derivative Operators, providing a rigo...

Fractional calculus of variations for double integrals

We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.

Some Iterated Integrals in the Fractional Calculus

Functional Integrals for Correlated Fermions

Functional integral methods provide a way to define mean–field theories and to systematically improve them. For the Hubbard model and similar strong–correlation problems, methods based in particular on the Hubbard–Stratonovich transformation have however been plagued by difficulties to formulate the problem in a spin–rotation invariant way. Here a formalism circumventing this problem by using a...

Motivic Integrals and Functional Equations

The functional equation for the motivic integral of Milnor number of a plane curve is derived using the Denef-Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to the multiplication by the constant and there is a simple algorithm to find its coefficients. The method is universal enough and gives, for example, the equations for t...