We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...

Let G0, . . . ,Gk be finite abelian groups, and let G0 ∗ · · · ∗ Gk be the join of the 0-dimensional complexes Gi . We give a characterization of the integral k-coboundaries of subcomplexes of G0 ∗ · · · ∗Gk in terms of the Fourier transform on the group G0 × · · · × Gk . This provides a short proof of an extension of a recent result of Musiker and Reiner on a topological interpretation of the ...

We analyse in three space-time dimensions, the connection between abelian self dual vector doublets and their counterparts containing both an explicit mass and a topological mass. Their correspondence is established in the lagrangian formalism using an operator approach as well as a path integral approach. A canonical hamiltonian analysis is presented, which also shows the equivalence with the ...

Let k be a number field, let E/k be an elliptic curve, and let S be a finite set of places of k containing the archimedean places. We prove that if α ∈ E(k) is nontorsion, then there are only finitely many torsion points ξ ∈ E(k)tors which are S-integral with respect to α. We also prove an analogue of this for the multiplicative group, and formulate conjectural generalizations for abelian varie...

We perform a path-integral analysis of the string representation of the dual Abelian Higgs (DAH) model beyond the London limit, where the string describing the vortex of a flux tube has a finite thickness. We show that besides an additional vortex core contribution to the string tension, a modified Yukawa interaction appears as a boundary contribution in the type-II dual superconducting vacuum....

The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D = 4, N = 4 SYM and used to construct the F 2 , F 4 and (F 5 + ∂ 2 F 4) terms in the effective action of coincident D-branes. The results are in agreement with those obtained by other methods. A simple derivation of the abelian ∂ 4 F 4 invariant is given and generalised to t...

The theme of doing quantum mechanics on all abelian groups goes back to Schwinger and Weyl. If the group is a vector space of finite dimension over a non-archimedean locally compact division ring, it is of interest to examine the structure of dynamical systems defined by Hamiltonians analogous to those encountered over the field of real numbers. In this letter a path integral formula for the im...

In this note we investigate the hypercentral units in integral group rings ZG, where G is not necessarily torsion. One of the main results obtained is the following (Theorem 3.5): if the set of torsion elements of G is a subgroup T of G and if Z2(U) is not contained in CU (T ), then T is either an Abelian group of exponent 4 or a Q∗ group. This extends our earlier result on torsion group rings.

Among the class of finite integral commutative residuated chains (ICRCs), we identify those algebras which can be obtained as a nuclear retraction of a conuclear contraction of a totally ordered Abelian l-group. We call the ICRCs satisfying this condition regular. Then we discuss the structure of finite regular ICRCs. Finally, we prove that the class of regular members generate a strictly small...

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2012-13/06c cpt ab gps.pdf] 1. Approximate identities on topological groups 2. Uniqueness of invariant measure 3. Simultaneous eigenfunctions for integral operators 4. Simultaneous eigenfunctions are characters The spectral theory for normal compact operators on Hil...