The quantisation of the reduced first-order dynamics of the nonrelativistic model for Chern– Simons vortices introduced by Manton is studied on a sphere of given radius. We perform geometric quantisation on the moduli space of static solutions, using a Kähler polarisation, to construct the quantum Hilbert space. Its dimension is related to the volume of the moduli space in the usual classical l...

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 construction of the kinematical Hilbert space and the implementation of the constraints. This leads to an explicit and very interesting relation between the a...

In this paper, we present a novel semi-classical theory of the electrostatic and magnetostatic fields explain nonlocality problem in context Aharonov-Bohm effect [1]. Specifically, show that possess quantum nature manifests if certain conditions are met. particular, wave amplitudes seen to exist even regions where classical vanish they operate on electron functions locally as unitary phases. Th...

We analyse the implications of the fact that there are two claims for a dual to N=4 superconformal SU(N) Yang-Mills theory (SCYM), the Maldacena conjecture and the theorem of Rehren. While the Maldacena dual is conjectured to be a non-perturbative string theory for large string coupling gs and small N , the Rehren dual is an ordinary quantum field theory on AdS5 for all values of the parameters...

We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the“canonical quantum spacetime”. The aim is to distinguish and compare the approaches under various points of vie...

The gauged Lorentz theory with torsion has been argued to have an effective whose non-trivial background is responsible for gravitational curvature if treated as a quantum-mechanical variable against of constant curvature. We use the CDG decomposition argue that such can be found without including torsion. Adapting our previously published Clairaut-based treatment QCD, we go on study implicatio...

These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract algebraic aspects of quantisation in contrast to more standard treatments of such issues, while also bridging towards the path integral formulation of quantisation. ...

We analyze the weak-field limit of General Relativity with matter and its possible quantisations. This analysis aims towards a predictive quantum theory to provide first-principles description gravitational effects in macroscopic systems. includes recently proposed experiments on generation (Newtonian) forces from distributions matter, phenomena like gravity-induced entanglement, cat states, Ra...