Abelian Gauge Field Theory Research Articles

Prescribing Zeros and Poles on a Compact Riemann Surface for a Gravitationally Coupled Abelian Gauge Field Theory

In this paper, we study the existence of prescribed cosmic strings and antistrings realized as the static solutions with prescribed zeros and poles of the Einstein equations coupled with the classical sigma model and an Abelian gauge field over a compact Riemann surface. We show that the equations of motion are equivalent to a system of self-dual equations and the presence of string defects are necessary and sufficient for gravitation which implies the equivalence of topology and geometry in the model. More precisely, we prove that the absence of a solution with zeros and poles implies that the underlying Riemann surface S must be a flat 2-torus and that the existence of a solution with zeros and poles implies that S must be a 2-sphere. Furthermore, we develop an existence theory for solutions with prescribed zeros and poles. We also obtain some nonexistence results.

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).

Causality and CPT violation from an Abelian Chern–Simons-like term

We study a class of generalized Abelian gauge field theories where CPT symmetry is violated by a Chern-Simons-like term which selects a preferred direction in spacetime. Such Chern-Simons-like terms may either emerge as part of the low-energy effective action of a more fundamental theory or be produced by chiral anomalies over a nonsimply connected spacetime manifold. Specifically, we investigate the issues of unitarity and causality. We find that the behaviour of these gauge field theories depends on whether the preferred direction is spacelike or timelike. For a purely spacelike preferred direction, a well-behaved Feynman propagator exists and microcausality holds, which indicates the possibility of a consistent quantization of the theory. For timelike preferred directions, unitarity or causality is violated and a consistent quantization does not seem to be possible.

The statistical mechanics of a concatenated polymer chain

The elastic and configurational properties of mesoscopic structures, which have been formed by linking a finite number of polymer loops to each other, are considered. For simplicity it is assumed that the linking numbers between pairs of loops provides a sufficient description of the topological structure. To conserve the topology the statistical mechanical calculation of the partition sum is restricted to the configuration space labelled by the specified linking numbers. An expansion of the partition sum is proposed where the linking numbers, corresponding to a particular structure, select a sub-set of terms from the expansion. The case of a linear concatenated chain of loops is studied and it is shown that the first non-zero contribution from this expansion is already able to describe the chain as a re-scaled Gaussian chain capable of supporting stress. This confirms that the approximation maintains the structural integrity of the chain. The effective step length and step length distribution function are also identified together with the elastic properties. The relationship of linking numbers to the Abelian Chern-Simons gauge field theory is used to illustrate essential parts of the calculation. The relevant term in the partition sum is represented in terms of Feynman diagrams describing the two-particle scattering amplitude for vector gauge bosons. It is shown that the expected re-scaled Gaussian chain result comes from the dominance in the s-channel of a massive scalar boson representing the structure of an individual loop in the chain.

Dual Description of U(1) Charged Fields in (2+1) Dimensions

We show that the functional bosonization procedure can be generalized in such a way that, to any field theory with a conserved Abelian charge in 2+1 dimensions, there corresponds a dual Abelian gauge field theory. The properties of this mapping and of the dual theory are discussed in detail, presenting different explicit examples. In particular, the meaning and effect of the coefficient of the Chern–Simons term in the dual action is interpreted in terms of the spin and statistics connection.

Spontaneous compactification of D=5 two-form gauge fields and the obtainment of Maxwell and Yang–Mills theories

We show that the spontaneous compactification of the Abelian and non-Abelian two-form gauge field theories from D=4+1 to D=3+1 leads to the same theories plus the Maxwell and Yang–Mills ones, respectively. The vector potential comes from the zero mode of the fifth component of the tensor gauge field in D=5. Concerning the non-Abelian case, it is necessary to make a more refined definition of the three-form stress tensor in order to be compatible, after the compactification, with the two-form stress tensor of the Yang–Mills theory.

GAUGE TRANSFORMATION PROPERTIES OF VECTOR AND TENSOR POTENTIALS REVISITED: A GROUP QUANTIZATION APPROACH

The possibility of nontrivial representations of the gauge group on wave functionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons. This is a non-Higgs mechanism that could provide new clues for the best understanding of the symmetry breaking mechanism in unified field theories. A unified quantization of massless and massive non-Abelian Yang–Mills, linear gravity and Abelian two-form gauge field theories are fully developed from this new approach, where a cohomological origin of mass is pointed out.

Abelian gauge theory on Riemann surfaces and new topological invariants

An Abelian gauge field theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the first Chern class c 1 (L) and by a certain intersection number obtained from the multivortices. We show that E = 2π(N + P). To realize such topological invariants as minimum energies, an existence and uniqueness theorem is established under the necessary and sufficient condition that |c 1 (L)| = |N − P|

Strings of opposite magnetic charges in a gauge field theory

We show that there are soliton–like solutions representing arbitrarily located M vortices and N antivortices with opposite magnetic charges in an Abelian gauge field theory. We establish an existence and uniqueness theorem and prove that the total magnetic flux is proportional to M − N but the total energy is proportional to M + N . In the presence of Einstein's gravity, we establish an existence theorem under a necessary and sufficient condition that ensures the geodesic completeness of the corresponding gravitational metric. The coexisting vortices and antivortices are now cosmic strings and antistrings and the total magnetic flux and matter–gauge energy are given by similar expressions as those for vortices. Besides the energy, the total curvature also provides an exact, quantized, measurement of the number of the strings of the two types.

Moving frames hierarchy and BF theory

We show that the one-dimensional projection of Chern–Simons gauged nonlinear Schrödinger model is equivalent to an Abelian gauge field theory of a continuum Heisenberg spin chain. In such a theory, the matter field has geometrical meaning of coordinates in tangent plane to the spin phase space, while the U(1) gauge symmetry relates to rotation in the plane. This allows us to construct the infinite hierarchy of integrable gauge theories and related magnetic models. To each of them a U(1) invariant gauge fixing constraint of non-Abelian BF theory is derived. The corresponding moving frames hierarchy is obtained and the spectral parameter is interpreted as a constant-valued statistical gauge potential constrained by the 1-cocycle condition.

Gauge field mass generation by toroidal spacetime

We consider an Abelian gauge field theory on the partially compactified spacetime , where is the N-dimensional torus and is a n-dimensional Riemannian manifold. The mass of the gauge field generated by quantum fluctuations of a massive or massless scalar field, minimally coupled to a constant background gauge potential, is the quantity of our main interest. As long as the eigenvalue spectrum of is positive (where is the Laplace--Beltrami operator of the manifold , R the Riemann scalar curvature and m the mass of the quantum field), it is found that the topologically generated mass is real for arbitrary N. If, however, the spectrum has zero eigenvalues we found that, depending on the compactification lengths of the torus, the generated mass may also be imaginary.

Topological gauge field mass generation by toroidal spacetime

The author considers an Abelian gauge field theory on Euclidean partially compactified spacetime TN*Rn for arbitrary N and n. The one-loop effective potential generated by quantum fluctuations of a massive scalar field, minimally coupled to a constant background Abelian gauge potential is calculated for arbitrary compactification lengths L1,. . .,LN of the multi-dimensional torus. In particular the topologically generated mass of the gauge field is obtained and its complicated dependence on the parameters involved (compactification lengths, mass M of the scalar field) is given explicitly. It is found that the topologically generated mass is positive for arbitrary N and n and that it does not depend on a renormalization parameter. For n>2 the limit M to 0 is smooth, but for n=0,1,2 zero modes play a crucial role and the generation of real or imaginary gauge field masses is possible.

Study of sphaleron transitions by means of the real-time Langevin equation.

Microscopic Langevin evolution is introduced in Abelian gauge field theory. It is studied numerically in the (1 + 1)-dimensional Abelian Higgs model at finite temperature. The Brownian behavior of the Chern-Simons number is established. Sharp transitions between the classical vacua with different Chern-Simons numbers are observed. The rate of these transitions depends exponentially on the temperature, indicating the relevance of the thermal activation theory involving the sphaleron saddle point.

Massive abelian gauge field theory and interaction between baryon charges and currents

A renormalizable and unitary massive abelian gauge field theory is proposed. It suggests a possible existence of the interaction between baryons and currents.

Aspects of QED and non-Abelian gauge theories in S1

We study various aspects of Abelian and non-Abelian gauge field theories in flat spacetime with the topology of ${S}^{1}$\ifmmode\times\else\texttimes\fi{}${R}^{n}$ (n=3,4). We first discuss the effective potential for the electromagnetic field in ${S}^{1}$\ifmmode\times\else\texttimes\fi{}${R}^{3}$ spacetime, with the objective of finding the dependence of coupling constants on the size L of the compactified dimension. It is first necessary to determine the stable vacuum. In particular, a charged scalar field satisfies an effective periodic boundary condition, while a charged spinor field satisfies an effective antiperiodic boundary condition at the stable vacuum. Then we study the effective coupling constants which depend on the size L of the compactified dimension at one-loop level for QED in ${S}^{1}$\ifmmode\times\else\texttimes\fi{}${R}^{3}$ spacetime. In the presence of a charged scalar field, the one-loop correction of one of the effective coupling constants for the lowest Fourier component of the electromagnetic field behaves for small L like 1/L, rather than lnL. This is because the lowest Fourier component of the scalar field is constant in the ${S}^{1}$ direction. The effective coupling constants for higher Fourier components have logarithmic L dependence, but due to collinear singularities (i.e., singularities in self-energy occurring in the limit of zero mass when the virtual particles are on shell and have parallel momenta) the coefficient of the lnL term differs from component to component. We also point out some ambiguities in defining the effective coupling constants. Finally we discuss the effective potential of non-Abelian gauge theories with a charged spinor field in ${S}^{1}$\ifmmode\times\else\texttimes\fi{}${R}^{4}$ spacetime. We find that if periodic boundary conditions are imposed on the spinor field in the beginning, the local gauge symmetry will be spontaneously broken in some cases, and we give an explicit model in which this occurs. This spontaneous symmetry breaking depends on the gauge group and its representations, and does not occur for an Abelian gauge field.

Local Gauge Invariance of Non-Abelian Gauge Field Theory

The non·abelian gauge field theory is formulated under a gauge fixing condition of non· differential form. The condition is characterized by two properties: (i) Time· like components of gauge fields are completely determined by the other components and source fields, as in the radiation gauge. (ii) Gauge functions are timely constant arbitrary functions, and then independent of field operators. The theory is proved to be form-invariant under local gauge transformations. Our formulation can be regarded as a legitimate formulation of an expedience in the radiation gauge formulation, where the field operator dependence of gauge functions is completely disregarded. Property (ii) makes our formulation deviate from the radiation gauge formulation to a large extent.

Compensation of perturbation anomalies in an abelian gauge field model

In the Abelian gauge field theory of an axial-vector meson coupled to a conserved axial current, one elaborates a mechanism first proposed by Adler, Gross and Jackiw to compensate the failure of the axial Ward identity by including an extra termO(g 3) in the Lagrangian density. This extra contribution is quantized first in a noncovariant gauge, along with the free-field contribution. A Lorentz-invariant form is then given and spontaneous symmetry breaking is shown to arise in higher orders.

Asymptotically-Free Abelian Gauge Field Theories with Indefinite Metric

Asymptotically-Free Abelian Gauge Field Theories with Indefinite Metric