On the Interquark Potential calculation from Dirac Brackets

We obtain the binding energy of an infinitely heavy quark-antiquark pair from Dirac brackets by computing the expectation value of the pure QCD Hamiltonian. This procedure exploits the rich structure of the dressing around static fermions. Some subtle points related to exhibing explicitly the interquark energy are considered.Comment: 9 pages, late

On the detection of relativistic magnetic monopoles by deep underwater and underice neutrino telescopes

I present here some reflections and very speculative remarks on the detection of relativistic magnetic monopoles by currently operating deep underwater/ice neutrino telescopes.Comment: To appear in the proceedings of the 5th International Workshop RICH200

Abelianization of First Class Constraints

We show that a given set of first class constraints becomes abelian if one maps each constraint to the surface of other constraints. There is no assumption that first class constraints satisfy a closed algebra. The explicit form of the projection map is obtained at least for irreducible first class constraints. Using this map we give a method to obtain gauge fixing conditions such that the set of abelian first class constraints and gauge fixing conditions satisfy the symplectic algebra.Comment: To appear in PL

Inequivalence of the Massive Vector Meson and Higgs Models on a Manifold with Boundary

The exact quantization of two models, the massive vector meson model and the Higgs model in the London limit, both describing massive photons, is presented. Even though naive arguments (based on gauge-fixing) may indicate the equivalence of these models, it is shown here that this is not true in general when we consider these theories on manifolds with boundaries. We show, in particular, that they are equivalent only for a special choice of the boundary conditions that we are allowed to impose on the fields.Comment: 14 pages, LATEX File (revised with minor corrections

Kahler Quantization of H3(CY3,R) and the Holomorphic Anomaly

Studying the quadratic field theory on seven dimensional spacetime constructed by a direct product of Calabi-Yau three-fold by a real time axis, with phase space being the third cohomology of the Calabi-Yau three-fold, the generators of translation along moduli directions of Calabi-Yau three-fold are constructed. The algebra of these generators is derived which take a simple form in canonical coordinates. Applying the Dirac method of quantization of second class constraint systems, we show that the Schr\"{o}dinger equations corresponding to these generators are equivalent to the holomorphic anomaly equations if one defines the action functional of the quadratic field theory with a proper factor one-half.Comment: 10 pages, few typos corrected, to appear in JHE

Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism

In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space.Comment: 12 page

Self-field, radiated energy, and radiated linear momentum of an accelerated point charge

Working within the framework of the classical theory of electrodynamics, we derive an exact mathematical solution to the problem of self-field (or radiation reaction) of an accelerated point-charge traveling in free space. We obtain relativistic expressions for the self-field as well as the rates of radiated energy and linear momentum without the need to renormalize the particle's mass - or to discard undesirable infinities.Comment: 18 pages, 31 equations, 16 references, 7 appendice

Atiyah-Singer Index Theorem in an SO(3) Yang-Mills-Higgs system and derivation of a charge quantization condition

The Atiyah-Singer index theorem is generalized to a two-dimensional SO(3) Yang-Mills-Higgs (YMH) system. The generalized theorem is proven by using the heat kernel method and a nonlinear realization of SU(2) gauge symmetry. This theorem is applied to the problem of deriving a charge quantization condition in the four-dimensional SO(3) YMH system with non-Abelian monopoles. The resulting quantization condition, eg=n (n: integer), for an electric charge e and a magnetic charge g is consistent with that found by Arafune, Freund and Goebel. It is shown that the integer n is half of the index of a Dirac operator.Comment: 18pages, no figures, minor corrections, published versio