It is argued that the low-energy dynamics of k monopoles in N=2 supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric quantum mechanics based on the moduli space of k static monople solutions. This generalises Manton’s “geodesic approximation” for studying the low-energy dynamics of (bosonic) BPS monopoles. We discuss some aspects of the quantisation and in particular argue t...

We examine various properties of double field theory and the doubled string sigma model in context geometric quantisation. In particular we look at T-duality as symplectic transformation related to an alternative choice polarisation construction quantum bundle for string. Following this perspective adopt a variety techniques from quantisation study space. One application is coherent state that ...

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality and M–theory, and it has been suggested that they should also have a counterpart in quantum mechanics. In view of these developments we propose dequantisati...

A recent concept in theoretical physics, motivated in string duality and M–theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation o...

The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. 2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under ...

We develop here a simple quantisation formalism that make use of Lie algebra properties of the Poisson bracket. When the brackets {H,φi} and {φi, φj}, where H is the Hamiltonian and φi are primary and secondary constraints, can be expressed as functions of H and φi themselves, the Poisson bracket defines a Poisson-Lie structure. When this algebra has a finite dimension a system of first order p...

Abstract We propose a “guide” towards quantisation of gravity based on quantum matter in statistical mechanics context. On one hand, model naturally arises from the thermodynamic interpretation horizons Rindler space. other path integral formulation field theory can be interpreted point view mechanics. From these perspectives, and are related to each same way as gas its chemical potential are. ...

We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear σ-model. Some new light is also shed on the Dirac bracket. Furthermore, it is shown how classical constraints not in involution with the classical Hamiltonian...

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrödinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with the probab...