The path integral for 3+1 abelian gauge theory is rewritten in terms of a real antisymmetric field allowing a dual action that couples the electric and magnetic currents to the photon and each other in a gauge invariant manner. Standard perturbative abelian quantum electrodynamics reemerges when the monopole current vanishes. For certain simple relationships between the monopole current and the...

In this short review main issues related to the non-Abelian Stokes theorem have been addressed. The two principal approaches to the non-Abelian Stokes theorem, operator and two variants (coherent-state and holomorphic) of the path-integral one, have been formulated in their simplest possible forms. A recent generalization for a knotted loop as well as a suggestion concerning higher-degree forms...

The Lie-Poisson structure of non-Abelian Thirring models is discussed and the Hamiltonian quantization of these theories is carried out. The consistency of the Hamiltonian quantization with the path integral method is established. It is shown that the space of non-Abelian Thirring models contains the nonperturbative conformal points which are in one-to-one correspondence with general solutions ...

Simulation of an Abelian Higgs theory in world line (polymer) representation. In World Line Path Integral representation Abelian Higgs theories admit a curvature term in the Hamiltonian. Using Monte Carlo simulations we show that the curvature term drives a phase transition at sufficiently strong coupling. In quenched approximation this phase transition is smooth, with implications that the mod...

Title of thesis: CLASSIFICATION OF PRIME IDEALS IN INTEGRAL GROUP ALGEBRAS OF FINITE ABELIAN GROUPS Heather Mallie McDonough, Master of Arts, 2005 Thesis directed by: Professor William Adams Department of Mathematics Let Z[G] be the integral group algebra of the group G. In this thesis, we consider the problem of determining all prime ideals of Z[G] where G is both finite and abelian. Because o...

Even though the (untwisted) Whitehead doubling operation kills all known abelian invariants of knots (and makes them topologically slice), we show that it does not kill the rational function that equals to the 2-loop part of the Kontsevich integral.

We present a very accurate formula counting norms of normal integral bases in tame abelian extensions of the rational eld. The methods used include applications of Schmidt's Subspace Theorem, Baker's Theorem and the Hardy-Littlewood Method, all from diophantine approximation.

The surface area of a general n-dimensional ellipsoid is represented as an Abelian integral, which can readily be evaluated numerically. If there are only 2 values for the semi-axes then the area is expressed as an elliptic integral, which reduces in most cases to elementary functions. The capacity of a general n-dimensional ellipsoid is represented as a hyperelliptic integral, which can readil...

We prove the integral Hodge conjecture for one-cycles on a principally polarized complex abelian variety whose minimal class is algebraic. In particular, Jacobian of smooth projective curve over numbers satisfies one-cycles. The main ingredient lift Fourier transform to Chow groups. Similarly, we Tate separable closure finitely generated field. Furthermore, varieties satisfying such are dense i...