Related papers: Dilatation Operator and Space-time Geometry
We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter $\sigma\,(0\leq\sigma\leq\beta)$. We point out new features which arise when $\sigma\neq…
Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We review aspects of quantisation of the 11-dimensional supermembrane world volume theory. We explicitly construct vertex operators for the massless states and study interactions of supermembranes. The open supermembrane and its vertex…
A study of the one loop dilatation operator in the scalar sector of $\cal N$ $=$ 4 SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the…
We review some of the geometry of the quantum projective plane with emphasis on the construction of a differential calculus and of the Dirac operator (of a spin^c-structure). We also report on anti-self-dual connections on line bundles, the…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
We will establish the connection between the Lorentz covariant and so-called single-time formulation for the quark Wigner operator. To this end we will discuss the initial value problem for the Wigner operator of a field theory and give a…
A realization of the elliptic quantum algebra $U_{q,p}(\widehat{sl_2})$ for any given level $k$ is constructed in terms of three free boson fields and their accompanying twisted partners. It can be viewed as the elliptic deformation of…
Generalised Wigner and Weyl transformations of quantum operators are defined and their properties, as well as those of the algebraic structure induced on the phase-space are studied. Using such transformations, quantum linear evolution…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations…
Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially…
We demonstrate how one can see quantization of geometry, and quantum algebraic structure in supersymmetric gauge theory.
We analyse the one-loop dilatation operator with the help of the Brauer algebra. We find some BPS operators in N=4 SYM, which are labelled by irreducible representations of the Brauer algebra. Some of them are quarter BPS operators. The…
The representations of position and momentum operators of a planar phase space having both position and momentum noncommutativity are obtained. Using these representations the dynamics of a particle in a gravitational quantum well is…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
We show that the time evolution of density operator of open qubit system can always be described in terms of the Kraus representation. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can…
We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase…