Related papers: Phase Space Reduction for Star-Products: An Explic…
We establish a general formula for the enclosed volume of constant mean curvature (CMC) surfaces in Euclidean three space with translational periods forming a lattice. The formula relates the volume to the surface area, a…
In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation in the simplicial case. We illustrate how this formalism can elucidate lattice…
Given two vectors $u,v \in \mathbb{Q}^D$ over a finite domain $D$ and a function $f : D\times D\to D$, the convolution problem asks to compute the vector $w \in \mathbb{Q}^D$ whose entries are defined by $w(d) = \sum_{\substack{x,y \in D \\…
We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G\ltimes g^*$ on a three-manifold of topology $R \times S$, where $S$ is a surface of genus $g$ with $n+1$ punctures. At each…
We extend our investigations on $\mathfrak g$-invariant Fedosov star products and quantum momentum mappings \cite{MN03a} to star products of Wick type on pseudo-K\"ahler manifolds. Star products of Wick type can be completely characterized…
We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection $P$ on a separable Hilbert space $\HH$, with the convergence in $L^2_\mathrm{loc}(\mathbb{R};\HH)$. It…
The star product technique translates the framework of local fields on noncommutative space-time into nonlocal fields on standard space-time. We consider the example of fields on $\kappa$- deformed Minkowski space, transforming under…
Suppose $k$ is a finite field, that $C$ is a smooth projective geometrically irreducible curve over $k$, and that $n$ is a positive integer not divisible by the characteristic of $k$. In this paper we compute cup products of elements of the…
According to a well-known result in geometric topology, we have \linebreak $\left (\mathbb{S}^2 \right)^{n}\!\!/\operatorname{Sym}(n) = \mathbb{CP}^{n}$, where $\operatorname{Sym}(n)$ acts on $\left (\mathbb{S}^2 \right)^{n}$ by coordinate…
In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of…
Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized…
We present a star product between differential forms to second order in the deformation parameter $\hbar$. The star product obtained is consistent with a graded differential Poisson algebra structure on a symplectic manifold. The form of…
We give a new explicit construction of $n\times N$ matrices satisfying the Restricted Isometry Property (RIP). Namely, for some c>0, large N and any n satisfying N^{1-c} < n < N, we construct RIP matrices of order k^{1/2+c}. This overcomes…
We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson…
The description of all deformation quantizations with separation of variables on a Kaehler manifold obtained in our earlier paper is used to identify the Fedosov star-product of Wick type constructed by M. Bordemann and S. Waldmann. This…
In the context of deformation quantization, there exist various procedures to deal with the quantization of a reduced space M_red. We shall be concerned here mainly with the classical Marsden-Weinstein reduction, assuming that we have a…
We recall some of the fundamental achievements of formal deformation quantization to argue that one of the most important remaining problems is the question of convergence. Here we discuss different approaches found in the literature so…
We develop a complete theory of non-formal deformation quantization exhibiting a nonzero minimal uncertainty in position. An appropriate integral formula for the star-product is introduced together with a suitable space of functions on…
We extend the definition of the star product introduced by Lunin and Maldacena to study marginal deformations of N=4 SYM. The essential difference from the latter is that instead of considering U(1)xU(1) non-R-symmetry, with charges in a…
The simplest nontrivial toy model of a classical SU(3) lattice gauge theory is studied in the Hamiltonian approach. By means of singular symplectic reduction, the reduced phase space is constructed. Two equivalent descriptions of this space…