Normal forms, inner products, and Maslov indices of general multimode squeezings

Hörmander-Kashiwara and Maslov indices

Given a finite-dimensional symplectic vector space, we first study the fundamentals group of the space of symplectomorphisms and the space of Lagrangians to construct Maslov indices of loops in these spaces. Then we introduce Hörmander-Kashiwara index of a Lagrangian triple and use it to define Maslov indices counting the number of intersections of two paths of Lagrangians or symplectomorphisms...

Anti-symplectic Involution and Maslov Indices

We carry out some first steps in setting up a theory for Lagrangian Floer theory, mimicking Seidel’s construction for Hamiltonian Floer homology [7], for the subgroup HamL(M,ω) of Ham(M,ω) which preserves the Lagrangian L. When the symplectic manifold M has anti-symplectic involution c and L is the fixed Lagrangian submanifold, we consider the subgroup Hamc(M,ω) which commute with c. In the lat...

Noncommutative Maslov Index and η-Forms

Stochastic area distributions: optimal trajectories, Maslov indices and asymptotic results

In this paper we study the semi-classical approximation for the distribution of area associated with (i) planar polymer rings constrained to enclose a fixed algebraic area and (ii) planar rings subject to an external electric field and constrained to enclose a fixed algebraic area. We demonstrate that the results are accurate in the asymptotic regime. Moreover, we also show that in case (i) it ...

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.