Abstract:
The spacetime dependent lagrangian formalism of references [1-2] is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field, viz. $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge). The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct D-brane actions. PACS:11.15.-q ; 11.27+d ; 11.10.Ef

Abstract:
Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both abelian and nonabelian dualities. We illustrate how (1)Dirac string solution (2)Dirac quantisation condition (3)t'Hooft-Polyakov monopole solutions and (4)a procedure emerges for obtaining {\it new} classical solutions of Yang-Mills (Y-M) theory. Moreover, these results occur in a way that is strongly reminiscent of the {\it holographic principle}.

Abstract:
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the two-point space, and the matrix geometry M_2(C). On the first, the graviton is described by a Higgs field, and on the second, it is described by a gauge field. We start with the partition function and calculate the propagator and Greens functions for the gravitons. The expectation values of distances are evaluated, and we discover that distances shrink with increasing graviton excitations. We find that adding fermions reduces the effects of the gravitational field. A comparison is also made with Rovelli's canonical quantisation approach, and with his idea of spectral path integrals. We include a brief discussion on the quantisation of a Riemannian manifold.

Abstract:
Three dyon solutions to the SU(2) Yang-Mills-Higgs system are presented. These solutions are obtained from the BPS dyon by allowing the gauge fields to be complex, or by letting the free parameter of the BPS solution become imaginary. In all cases however the physically measurable quantities connected with these new solutions are entirely real. Although the new solutions are mathematically simple variations of the BPS solution, they have one or more physically distinct characteristics.

Abstract:
Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 black hole spacetime should be absent. General argument establishing the absence of real particle creation by AdS_3 black hole spacetime for this case of conformal triviality is provided. Then next, using the explicit mode expansion forms for conformally-coupled scalar and spinor fields, the bosonic and fermionic superradiances are examined and found to be absent confirming the expectation.

Abstract:
In this paper we develop the nonrelativistic quantum analysis of the charged particle-dyon system in the spacetime produced by an idealized cosmic string. In order to do that, we assume that the dyon is superposed to the cosmic string. Considering this peculiar configuration {\it conical} monopole harmonics are constructed, which are a generalizations of previous monopole harmonics obtained by Wu and Yang(1976 {\it Nucl. Phys. B} {\bf 107} 365) defined on a conical three-geometry. Bound and scattering wave functions are explicitly derived. As to bound states, we present the energy spectrum of the system, and analyze how the presence of the topological defect modifies obtained result. We also analyze this system admitting the presence of an extra isotropic harmonic potential acting on the particle. We show that the presence of this potential produces significant changes in the energy spectrum of the system.

Abstract:
We construct a dyon solution for the noncommutative version of the Yang-Mills-Higgs model with a -term. Extending the Noether method to the case of a noncommutative gauge theory, we analyze the effect of CP violation induced both by the -term and by noncommutativity proving that the Witten effect formula for the dyon charge remains the same as in ordinary space.

Abstract:
We consider vortex-type solutions in $d=5$ dimensions of the Einstein gravity coupled to a nonabelian SU(2) field posessing a nonzero electric part. After the dimensional reduction, this corresponds to a $d=4$ Einstein-Yang-Mills-Higgs-U(1)-dilaton model. A general axially symmetric ansatz is presented, and the properties of the spherically symmetric solutions are analysed.

Abstract:
The problem of separation of variables in a dyon--dyon system is discussed. A linear transformation is obtained between fundamental bases of this system. Comparison of the dyon--dyon system with a 4D isotropic oscillator is carried out.

Abstract:
The formalism of spacetime dependent lagrangians developed in Ref.1 is applied to the Sine Gordon and massive Thirring models.It is shown that the well-known equivalence of these models (in the context of weak-strong duality) can be understood in this approach from the same considerations as described in [1] for electromagnetic duality. A further new result is that all these can be naturally linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of {\it noncommuting coodinates} residing on the boundaries. PACS: 11.15.-q: 11.10/Ef