Abelian Theory Research Articles

Gauge link structure in quark–quark correlators in hard processes

Distribution functions in hard processes can be described by quark–quark correlators, nonlocal matrix elements of quark fields. Color gauge invariance requires inclusion of appropriate gauge links in these correlators. For transverse momentum dependent distribution functions, in particular important for describing T-odd effects in hard processes, we find that new link structures containing loops can appear in Abelian and non-Abelian theories. In transverse moments, e.g., measured in azimuthal asymmetries, these loops may enhance the contribution of gluonic poles. Some explicit results for the link structure are given in high-energy leptoproduction and hadron–hadron scattering.

On electric and magnetic charges in gauge theories

In this talk we will summarise a systematic approach to constructing physical, i.e., gauge-invariant, fields describing charged particles. We will show that this can be done in a well defined way in abelian theories and perturbatively in non-abelian theories. Various perturbative tests in three and four dimensions will be reported. The existence of a non-perturbative obstruction to the observability of quarks will be demonstrated. Finally the extension to magnetic charges is discussed and their non-existence in pure SU(2) is shown.

A generalization of Weyl's identity for Dn

The expansion in Schur functions of the product ∏ i< j (1− x i x j ) is well known. It is more or less equivalent to Weyl's identity for root-systems of type D n . In this paper we obtain the expansion in Schur functions of the product ∏ i< j (1−∑ ℓ>0 a ℓ x i x j ( x i ℓ− x j ℓ)/( x i − x j )), thus generalizing Weyl's identity. We obtain this result by systematic calculation in fermionic Fock space. But familiarity with the latter is not a prerequisite for reading this paper. We develop from scratch the modest amount of theory that we need in elementary and purely algebraic fashion, taking pains to integrate the theory with classical symmetric function theory. The tools developed in this paper ought to have many further applications, e.g., to random matrix theory and to computational abelian function theory.

Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic properties. The unusual physics of these systems is due to local constraints on the degrees of freedom which are variables localized on the links of the lattice. We discuss two types of constraints that become equivalent after a duality transformation for Abelian theories but are qualitatively different for non-Abelian ones. We emphasize highly nontrivial topological properties of the excitations (fluxons and charges) in these non-Abelian discrete lattice gauge theories. We show that an implementation of these models may provide one with the realization of an ideal quantum computer, that is the computer that is protected from the noise and allows a full set of precise manipulations required for quantum computations. We suggest a few designs of the Josephson-junction arrays that provide the experimental implementations of these models and discuss the physical restrictions on the parameters of their junctions.

Trace Anomalies and Chiral Ward Identities

In a simple Abelian spinor field theory, the canonical trace identitiesfor certain axial-vector and axial-scalar operators are re-examined indimensional regularization, some disagreements with previous results arefound and an interesting new phenomenon is observed and brieflydiscussed.

The helicity modulus in Abelian gauge field theories

We consider the 4d compact U(1) theory with Wilson action and characterize its phase diagram using the notion of electromagnetic flux, instead of the more usual magnetic monopole. Taking inspiration from the flux picture, we consider the helicity modulus (h.m.) for this theory, and show that it is an order parameter for the confinement deconfinement phase transition. We extend the definition of the h.m. to an Abelian projected Yang-Mills theory, and discuss its behavior in SU(2).

The 3-by-3 lemma for regular Goursat categories

We prove a 3 £ 3 lemma for regular Goursat categories. The classical “3 £ 3 lemma” in abelian category theory involves short exact sequences. In more general contexts — in particular in a category which is not pointed — it makes sense to replace short exact sequences by “exact forks”: these are diagrams R r1 / r2 / A r / B

Four-dimensional couplings among BF and matter theories from BRST cohomology

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a “free” model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.

Four‐dimensional couplings among BF and matter theories from BRST cohomology

AbstractThe local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a “free” model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.

Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians

The spacetime dependent Lagrangian formalism of Refs. 1 and 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. ϕa = 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 noncommuting coordinates on the boundary of the theory which may be used to construct D-brane actions. The formalism is also used to obtain the Deser–Gomberoff–Henneaux–Teitelboim results10 for dyon charge quantisation in Abelian p-form theories in dimensions D = 2(p+1) for both even and odd p.

Abelian and nonabelian vector field effective actions from string field theory

The leading terms in the tree-level effective action for the massless fields of the bosonic open string are calculated by integrating out all massive fields in Witten's cubic string field theory. In both the abelian and nonabelian theories, field redefinitions make it possible to express the effective action in terms of the conventional field strength. The resulting actions reproduce the leading terms in the abelian and nonabelian Born-Infeld theories, and include (covariant) derivative corrections.

On the dimensional dependence of duality groups for massive p-forms

We study the soldering formalism in the context of Abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia–Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even-dimensional spacetimes, in this way confirming the Higgs/Julia–Toulouse duality proposed by Quevedo and Trugenberger [Nucl. Phys. B 501 (1997) 143] a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.

On Abelian multi-Chern Simons field theories

In this paper a class of multi-Chern–Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general procedure is presented to eliminate the Chern–Simons fields from their action. In this way it has been possible to derive an expression of the partition function of topologically linked polymers which depends explicitly on the topological numbers and does not have intractable nonlocal terms as it happened in previous approaches. The new formulation of multi-Chern–Simons field theories is then used to remove and clarify some inconsistencies and ambiguities which apparently affect field theoretical models of topologically linked polymers. Finally, the limit of disentangled polymers is discussed.

Fermionic and scalar corrections for the Abelian form factor at two loops

Two-loop corrections for the form factor in a massive Abelian theory are evaluated, which result from the insertion of massless fermion or scalar loops into the massive gauge boson propagator. The result is valid for arbitrary energies and gauge boson mass. Power-suppressed terms vanish rapidly in the high-energy region where the result is well approximated by a polynomial of third order in ln(s/M2). The relative importance of subleading logarithms is emphasized.

Quasi-closed primary components in abelian group rings

All groups considered in this work are assumed to be multiplicatively written abelian groups and all rings are commutative with identity of prime characteristic p for some fixed prime p. We follow essentially throughout the notation and terminology to the abelian group theory of the excellent classical monographs of L. Fuchs [8]. All topological references are to the p-adic topology. For G a group and R a ring, RG will denote a group ring with a normed Sylow p-subgroup S(RG), which is in the focus of our interest. The notations and terminology from the commutative group algebras theory of the nice book of G. Karpilovsky [10] will be followed. This paper is a supplement and a generalization to our previous articles [6, 7]. The main purpose that motivates the present research is the global investigation of the quasicompleteness of S(RG) for large R and G on their minimal restrictions. In particular, as corollaries to our main results, we will obtain well-documented facts in [7] and other given by us in [6]. Before proving the central theorems, we need in the sequel some assertions stated in the following paragraph.

Abelian Groups at New Mexico State University

This is a description of some of the happenings in Abelian group theory at New Mexico State University (NMSU). This account is quite personal, and certainly has my own personal biases in it. Some of the players may feel slighted, for which I apologize. My excuses are simply bad memory and bad judgement. This account is supposed to explain how New Mexico State University became a center of Abelian group theory. At least it will describe some of the events and circumstances that I feel contributed to its development. There will be no attempt to detail who proved what particular theorem when, or to give a complete story of which areas were being emphasized at any particular time. Over the years, there were many Abelian group theorists at New Mexico State University doing many di¤erent things, and such a task would be overwhelming. Please keep these things in mind while reading this account. The ‡ourishing of Abelian group theory at New Mexico State was a product of several things. We had a sympathetic administration, both at the department level and at higher levels. Research money was readily available in the late 1950’s and 1960’s. And the subject was ready for development: Kaplansky’s book In nite Abelian Groups appeared in 1954, and Fuchs’book Abelian Groups appeared in 1958, and were tremendous catalysts. These circumstances and some good luck enabled us to attract some truly talented people. But how did this all get started, and how did New Mexico State continue to develop as a center of Abelian groups? It could be said that it was due to Professor W. R. Scott at the University of Kansas. At least four of his students came to NMSU after nishing at Kansas: Ralph Crouch, Delmar Boyer, me, and John Irwin, in that order. Boyer and I were recruited by Crouch, and I think John Irwin came because he wanted to go somewhere where there was another Abelian group theorist, and Professor Scott knew us. I came to NMSU in 1957, and Irwin in 1960. John was a very special person. He was intense, and totally devoted to the subject. He and I worked together for several years, at rst on his topic of high subgroups. I think John had as much to do with New Mexico State University becoming a center of Abelian groups as anyone. It was John who suggested that we apply for National Science

Abelian Group Theory in Italy

Abelian Group Theory in Italy

The Affinity of Set Theory and Abelian Group Theory

This paper reviews the uses of set theory to solve some long-standing problems in a number of different areas of abelian group theory. In some cases the solution is an independence result (from ZFC, the ordinary axioms of set theory); in other cases the result is a theorem of ZFC proved by combinatorial methods. In the interests of breadth, and to keep within the prescribed bounds of space, some depth and detail have been sacrificed and the emphasis is on key developments in the early history of each area. In general, except for Butler groups, a cut-off date of about 1990 has been observed, except for brief references to selected later developments. Also, for reasons of space, the bibliography is not complete.

Erratum: Equivalence of the self-dual model and Maxwell-Chern-Simons theory on arbitrary manifolds [Phys. Rev. D59, 065019 (1999)

Using a group-invariant version of the Faddeev-Popov method we explicitly obtain the partition functions of the Self-Dual Model and Maxwell-Chern-Simons theory. We show that their ratio coincides with the partition function of abelian Chern-Simons theory to within a phase factor depending on the geometrical properties of the manifold.

First and second order vortex dynamics

The low energy dynamics of vortices in selfdual Abelian Higgs theory is of second order in vortex velocity and characterized by the moduli space metric. When Chern-Simons term with small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provides an additional check of the first and second order terms by studying the angular momentum in the field theory. We briefly explore other first order term due to small background electric charge density and also the harmonic potential well for vortices given by the moment of inertia.