Related papers: Phase Space and Quantization of 2D BF Theory Coupl…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
We relate three-dimensional loop quantum gravity to the combinatorial quantisation formalism based on the Chern-Simons formulation for three-dimensional Lorentzian and Euclidean gravity with vanishing cosmological constant. We compare the…
We construct explicitly the quantization of classical linear maps of $SL(2, R)$ on toroidal phase space, of arbitrary modulus, using the holomorphic (chiral) version of the metaplectic representation. We show that Finite Quantum Mechanics…
For a 3D N=4 gauge theory, turning on the $\Omega$-background in RxR$^2_{\epsilon}$ deforms the Coulomb branch chiral ring into the quantum Coulomb branch algebra, generated by the 1/2-BPS monopoles together with the complex scalar in the…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
One of the methods proposed in the last years for studying non-perturbative gauge theory physics is quantum simulation, where lattice gauge theories are mapped onto quantum devices which can be built in the laboratory, or quantum computers.…
We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB.…
We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch,…
For $\g=sl(n)$ we construct a two parametric $U_h(\g)$-invariant family of algebras, $(S\g)_{t,h}$, which defines a quantization of the function algebra $S\g$ on the coadjoint representation and in the parameter $t$ gives a quantization of…
Loop Quantum Gravity (LQG) is one of the leading approaches to unify quantum physics and General Relativity (GR). The Hilbert space of LQG is spanned by spin-networks which describe the local geometry of quantum space-time. Simulation of…
We present a polymer(loop) quantization of a two dimensional theory of dilatonic gravity known as the CGHS model. We recast the theory as a parametrized free field theory on a flat 2-dimensional spacetime and quantize the resulting phase…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
An Abelian gerbe is constructed over classical phase space. The 2-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Poincare-Cartan form. The U(1) gauge group on the gerbe has a…
The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied…
The role of a physical phase space structure in a classical and quantum dynamics of gauge theories is emphasized. In particular, the gauge orbit space of Yang-Mills theories on a cylindrical spacetime (space is compactified to a circle) is…
We propose a construction of the quantum-corrected Coulomb branch of a general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the…