Related papers: Mould Calculus for Hamiltonian Vector Fields
We construct a gauge theory on a noncommutative homogeneous K\"ahler manifold, where we employ the deformation quantization with separation of variables for K\"ahler manifolds formulated by Karabegov. A key point in this construction is to…
We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain…
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\tau$-function and formal…
We compute the stable homology of orthogonal and symplectic groups over a finite field k with coefficients coming from an usual endofunctor F of k-vector spaces (exterior, symmetric, divided powers...), that is, for all natural integer i,…
Let ${\mathcal M}$ be a moduli space of stable vector bundles of rank $r$ and determinant $\xi$ on a compact Riemann surface $X$. Fix a semistable holomorphic vector bundle $F$ on $X$ such that $\chi(E\otimes F)= 0$ for $E \in \mathcal M$.…
We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…
For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…
We use the theory of selfdual Lagrangians to give a variational approach to the homogenization of equations in divergence form, that are driven by a periodic family of maximal monotone vector fields. The approach has the advantage of using…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour $C$. For a special class of contours the gauge condition reduces to…
Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In…
We study the sheaves of logarithmic vector fields along smooth cubic curves in the projective plane, and prove a Torelli-type theorem in the sense of Dolgachev-Kapranov for those with non-vanishing j-invariants.
We present a canonical quantization of electromagnetic modes in cylindrical waveguides, extending a gauge-based formalism previously developed for Cartesian geometries [1]. By introducing the two field quadratures $X,Y$ of TEM (transverse…
The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant…
In $n$-dimensional classical field theory one studies maps from $n$-dimensional manifolds in such a way that classical mechanics is recovered for $n=1$. In previous papers we have shown that the standard polysymplectic framework in which…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that…
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the…
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…
In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called…