In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of grouptheoretical techniques and then we give a possible way to solve the no-go theorem of ...

In this paper, we present new results on Temporal Decomposition (TD) applied to the Line Spectral Frequencies (LSFs) derived for wideband speech. The paper shows that by incorporating a dynamic programming search algorithm into TD, near transparent quantisation of wideband LSFs can be obtained at approximately 1 kbps. We also show that TD performs significantly better than Split Vector Quantisa...

Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding analytic expressions for a number of periodic states and determining their linear stability. Numerical evidence is given for nonlinear stability of some of these...

Mathematical modeling should present a consistent description of physical phenomena. We illustrate an inconsistency with two Hamiltonians – the standard Hamiltonian and an example found in Goldstein – for the simple harmonic oscillator and its quantisation. Both descriptions are rich in Lie point symmetries and so one can calculate many Jacobi Last Multipliers and therefore Lagrangians. The Las...

We quantise a Poisson structure on Hn+2g, where H is a semidirect product group of the form G ⋉ g. This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group G ⋉ g on R × Sg,n, where Sg,n is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with...

Outlier (or anomaly) detection is an important problem for many domains, including fraud detection, risk analysis, network intrusion and medical diagnosis, and the discovery of significant outliers is becoming an integral aspect of data mining. This paper presents CURIO, a novel algorithm that uses quantisation and implied distance metrics to provide a fast algorithm that is linear for the numb...