Related papers: Representations of the Quantum Holonomy-Diffeomorp…
Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a…
We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…
Quantifying quantum resources for simulating the fundamental forces of Nature is sensitive to the mapping of gauge fields onto finite quantum computational architectures. When locally truncating lattice gauge theories in the irreducible…
Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly…
The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
We study finite-dimensional representations of the Kauffman skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter q is a root of unity. The main one of these…
A quantum algorithm of SU(N) Yang-Mills theory is formulated in terms of quantum circuits. It can nonperturbatively calculate the Dyson series and scattering amplitudes with polynomial complexity. The gauge fields in the interaction picture…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper…
We survey several mathematical developments in the holonomy approach to gauge theory. A cornerstone of this approach is the introduction of group structures on spaces of based loops on a smooth manifold, relying on certain homotopy…
In loop quantum cosmology, one has to make a choice of SU(2) irreducible representation in which to compute holonomies and regularize the curvature of the connection. The systematic choice made in the literature is to work in the…
We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation…
Contour gauges are discussed in the framework of canonical formalism. We find flux operator algebras with the structure constants of underlying Yang-Mills theory.
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…