Related papers: Quantum Observables of Quantized Fluxes
We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying…
In this paper it is shown that a quantum observable algebra, the Heisenberg-Weyl algebra, is just given as the Hopf algebraic dual to the classical observable algebra over classical phase space and the Plank constant is included in this…
We study the effect of Aharonov-Bohm flux on the superconducting state in metallic cylinders. Although Byers and Yang attributed flux quantization to the flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown that…
New clues for the best understanding of the nature of the symmetry-breaking mechanism are revealed in this paper. A revision of the standard gauge transformation properties of Yang-Mills fields, according to a group approach to quantization…
Electromagnetism can be generalized to Yang-Mills theory by replacing the group U(1)$ by a nonabelian Lie group. This raises the question of whether one can similarly generalize 2-form electromagnetism to a kind of "higher-dimensional…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the…
We describe a finite analogue of the Poisson algebra of Wilson loops in Yang-Mills theory. It is shown that this algebra arises in an apparently completely different context; as a Lie algebra of vector fields on a non-commutative space.…
We analyze quantum Yang-Mills theory on $\mathbb{R}^2$ using a novel discretization method based on an algebraic analogue of stochastic calculus. Such an analogue involves working with "Gaussian" free fields whose covariance matrix is…
For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasi-particles.…
We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the stochastic quantisation equations of Yang-Mills on two and three dimensional Euclidean space with finite volume. The main result of these works is that one can…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…
Generalized flag manifolds endowed with the Bruhat-Poisson bracket are compact Poisson homogeneous spaces, whose decompositions in symplectic leaves coincide with their stratifications in Schubert cells. In this note it is proved that the…
Witten's observables of topological Yang-Mills theory, defined as classes of an equivariant cohomology, are reobtained as the BRST cohomology classes of a superspace version of the theory.
The mathematical structure of homogeneous loop quantum cosmology is analyzed, starting with and taking into account the general classification of homogeneous connections not restricted to be Abelian. As a first consequence, it is seen that…
The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved…
In this paper, we present a non-geometrodynamic quantum Yang-Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the…
Review of the papers on the new method of the Yang-Mills field quantization applicable both in perturbation theory and beyond it is presented. It is shown that in the modified formulation of the Yang-Mills theory leading to the formal…
We consider some typical gauge models in the causal approach: Yang-Mills and pure massless gravity up to the second order of the perturbation theory. We prove that the loop contributions are coboundaries, up to super-renormalizable terms in…
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra…