Related papers: Quantum Nonabelian Monopoles
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…
We study the classical and quantum motion of a relativistic charged particle on the spacetime produced by a global monopole. The self-potential, which is present in this spacetime, is considered as an external electrostatic potential. We…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
By the application of $\phi$-mapping topological theory, the properties of vortices in quantum R\"ontgen effect is thoroughly studied. The explicit expression of the vorticity is obtained, wherein which the $\delta$ function indicates that…
We study hyperbolic curves and their Jacobians over finite fields in the context of anabelian geometry.
We perform a numerical analysis of the gravitational field of a global monopole coupled nonminimally to gravity, and find that, for some given nonminimal couplings (in constrast with the minimal coupling case), there is an attractive region…
A non-symplectic generalization of Hamiltonian mechanics is considered. It allows include into consideration "non-Lagrange" systems, such as theory of charged particle in the field of magnetic monopole. The corresponding generalization for…
We study gauged Laplacian operators on line bundles on a quantum 2-dimensional sphere. Symmetry under the (co)-action of a quantum group allows for their complete diagonalization. These operators describe `excitations moving on the quantum…
The monopole for the geometric curvature is studied for non-Hermitian systems. We find that the monopole contains not only the exceptional points but also branch cuts. As the mathematical choice of branch cut in the complex plane is rather…
The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It…
We propose a new vector potential for the Abelian magnetic monopole. The potential is non-singular in the entire region around the monopole. We argue how the Dirac quantization condition can be derived for any choice of potential.
In this Reply I present some arguments in favor of the stability of the topological defect composed by global and magnetic monopoles.
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a…
Recent progress in the study of solitons and black holes in non-Abelian field theories coupled to gravity is reviewed. New topics include gravitational binding of monopoles, black holes with non-trivial topology, Lue-Weinberg bifurcation,…
Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which describe the dynamics of field singularities using gauge fields.…
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against…
Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number.…