Related papers: Monopole-based quantization: a programme
The Weyl modules in the sense of V.Chari and A.Pressley [CP] over the current Lie algebra on an affine variety are studied. We show that local Weyl modules are finite-dimensional and generalize the tensor product decomposition theorem from…
Magnetic monopoles are studied in the context of a Two Measure Field Theory.
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the…
The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable…
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be…
We discuss particle entanglement in systems of indistinguishable bosons and fermions, in finite Hilbert spaces, with focus on operational measures of quantum correlations. We show how to use von Neumann entropy, Negativity and entanglement…
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases…
I give a theoretical overview of magnetic monopoles, focusing on the physical perspective of monopoles as hypothetical particles rather than as mathematical objects. I argue that monopoles are exceptionally interesting hypothetical…
We quantize a generalized electromagnetism in 2 + 1 dimensions which contains a higher-order derivative term by using Dirac's method. By introducing auxiliary fields we transform the original theory in a lower-order derivative one which can…
The theory of Toeplitz quantization presented in our previous paper is extended and further developed to include diverse and interesting non-commutative realizations of the classical Euclidean plane. This is done using Hilbert spaces of…
In this article the simple modules over the rank-two quantized Weyl algebras at roots of unity over an algebraically closed field are classified.
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…
A higher level analog of Weyl modules over multi-variable currents is proposed. It is shown that the sum of their dual spaces form a commutative algebra. The structure of these modules and the geometry of the projective spectrum of this…
The MoEDAL experiment at the LHC is optimised to detect highly-ionising particles such as magnetic monopoles, dyons and (multiply) electrically-charged stable massive particles predicted in a number of theoretical scenarios. MoEDAL,…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite…
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…