相关论文: Noncommutative Symmetric Functions and Lagrange In…

We present a formulation in a curved background of noncommutative mechanics, where the object of noncommutativity $\theta^{\mu\nu}$ is considered as an independent quantity having a canonical conjugate momentum. We introduced a…

In this paper we construct a noncommutative space of ``pointed Drinfeld modules'' that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of…

We present a conspicuous number of indefinite integrals involving Heun functions and their products obtained by means of the Lagrangian formulation of a general homogeneous linear ordinary differential equation. As a by-product we also…

We revisit Wigner's question about the admissible commutation relations for coordinate and velocity operators given their equations of motion (EOM). In more general terms we want to consider the question of how to quantize dynamically…

Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used…

In an attempt to look for the root of nonstandard Lagrangians in the theories of the inverse variational problem we introduce a logarithmic Lagrangian (LL) in addition to the so-called reciprocal Lagrangian (RL) that exists in the…

One of the simplest example of non-commutative (NC) spaces is the NC plane. In this article we investigate the consequences of the non-commutativity to the quantum mechanics on a plane. We derive corrections to the standard (commutative)…

We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…

Let $G$ be a compact, connected Lie group and $T \subset G$ a maximal torus. Let $(M,\omega)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra…

We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green's functions is found in all directions. To this end, we first determine a kernel functional equation connecting…

Thermofield dynamics is presented in terms of a path-integral using coherent states, equivalently, using a coadjoint orbit action. A field theoretic formulation in terms of fields on a manifold ${\mathcal M} \times {\tilde{\mathcal M}}$…

Let $n \in \mathbb{Z}_{\geq 3}$ be given. We prove Lebesgue-almost everywhere pointwise inversion formulae for the Siegel transforms in the geometry of numbers. These inversion formulae are quite general; for instance, they are valid for…

Surface charges and their algebra in interacting Lagrangian gauge field theories are investigated by using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

The inverse problem of fractional Brownian motion and other Gaussian processes with stationary increments involves inverting an infinite hermitian positively definite Toeplitz matrix (a matrix that has equal elements along its diagonals).…

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…

Let $K$ be any unital commutative $\bQ$-algebra and $z=(z_1, z_2, ..., z_n)$ commutative or noncommutative variables. Let $t$ be a formal central parameter and $\kttzz$ the formal power series algebra of $z$ over $K[[t]]$. In \cite{GTS-II},…

In this paper, the theory of smooth action-dependent Lagrangian mechanics (also known as contact Lagrangians) is extended to a non-smooth context appropriate for collision problems. In particular, we develop a Herglotz variational principle…

We show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\mathbb{R}^3_\lambda$ and the components of…

In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Witten's conjectures, can be described completely algebraically as the homology of a certain…