External Gauge Field Research Articles

Anomaly constraints on nonlinear sigma models

Anomalies in nonlinear sigma models can sometimes be cancelled by local counterterms. We show that these counterterms have a simple topological interpretation, and that the requirements for anomaly cancellation can be easily understood in terms of 't Hooft's anomaly matching conditions. We exhibit the anomaly cancellation on homogeneous spaces G H and on general riemannian manifolds M . We include external gauge fields on the manifolds and derive the generalized anomaly-cancellation conditions. Finally, we discuss the implications of this work for superstring theories.

Semiclassical approach to Dirac operators in external gauge fields corresponding to supersymmetric quantum systems.

We show that for the class of gauge-field configurations which reduce the Dirac operator to the one-dimensional Witten Hamiltonian, an appropriate semiclassical quantization rule permits the computation of the bound-state spectrum in an accurate way.

Anomalies and odd dimensions

The parity-violating effective action for theories of fermions coupled to external gauge and gravitational fields in odd dimensions is computed exactly. This action is then used to compute gauge and gravitational anomalies in even dimensions. This derivation of the anomalies elucidates the relation of covariant to consistent anomalies as well as the relation between the Abelian anomaly and the non-Abelian anomaly in two lower dimensions.

Propagators for lattice gauge theories in a background field

We prove regularity and decay properties for propagators connected with the renormalization group method in lattice gauge theories. These propagators depend on an external gauge field configuration, called a background field.

Exact solutions of the Dirac equations in external non-Abel gauge fields

This paper presents solutions to the Dirac equation for particles with isospin T = 1/2 in field defined by non-Abel potentials of two types. The first type consists of constant potentials defining a chromomagnetic field directed along the third isotopic axis; the second type describes plane waves of elliptical polarization. The tensors of fields of both types can be related to a gauge transform of the type where a local revolution is expressed in isospin space.

Special symmetries for the Utiyama Lagrangian with external Yang-Mills fields.

This paper demonstrates how conditions for the existence of symmetries for particles interacting with external background gauge fields arise easily from the standard symmetry equations. The general phenomenon is described by the Lagrangian ${L}_{\mathrm{UA}}$ obtained from Utiyama's original Lagrangian ${L}_{U}$ by regarding the gauge fields A as a given set of fields. An infinitesimal transformation X+Y, consisting of certain combined infinitesimal coordinate and local gauge transformations, will be an infinitesimal symmetry of ${L}_{\mathrm{UA}}$ precisely when the Lie derivative (${\mathrm{L}}_{\mathrm{UA}}$) yields a Lagrangian with identically vanishing Euler-Lagrange equations. This Lie derivative is explicitly computed and is shown to contain the expressions derived recently by several papers in the literature, as well as a new expression with possible physical importance.

Harmonic expansions and quasi-riemannian geometry in Kaluza-Klein theories

Since Kaluza-Klein supergravity does not contain the observed particles as elementary fields, alternative approaches in Kaluza-Klein theories without external gauge fields may be considered. We take up Weinberg's suggestion of changing the tangent space group and we find that some or all of the gauge field strengths associated with isometry group vanish unless there is torsion.

Spinor analysis of Yang-Mills theory in the Minkowski space

Self-duality equations for Yang-Mills fields and the Dirac equation with an external (anti-) selfdual gauge field are studied in the Minkowski space by spinorial methods. For the Dirac equations, all (four) possible combinations of the fermion chirality and duality of the external fields are considered.

Charged particles with electromagnetic interactions and U(1)-gauge theory: Hamiltonian and Lagrangian formalisms

The motion of charged particles in external electromagnetic fields is reviewed with the purpose of determining the whole set of constants of motion. The Johnson-Lippmann results concerning the interaction with a constant magnetic field are taken as the starting point of the study. Our results are obtained through simple group-theoretical arguments based essentially on extended Lie algebras associated with the kinematical group of the (constant) electromagnetic field involved in the interaction. Nonrelativistic Schr\"odinger (or Pauli) and relativistic Dirac Hamiltonians are considered. The corresponding Lagrangian densities are then studied when the charged particles move in arbitrary electromagnetic fields. Through Noether's theorem, we get the constants of motion when coordinate and gauge transformations are combined. These results complete the U(1)-gauge theory and relate the works of Bacry, Combe, and Richard and of Jackiw and Manton when external gauge fields are considered. These developments enhance the minimal-coupling principle, the U(1)-gauge theory, and Noether's theorem.

A note on the Atiyah-Singer index theorem

A new proof of the Atiyah-Singer index theorem for the Dirac equation in the presence of external gauge and gravitational field is presented.

Regularity and decay of lattice Green's functions

In the paper we study a class of lattice, covariant Laplace operators with external gauge fields. We prove that these operators are positive and that their Green's functions decay exponentially. They also have regularity properties similar to continuous space Green's functions. All the bounds are uniform in the lattice spacing.

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU( N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.

The axial anomaly and the lattice Dirac sea

In the hamiltonian formulation of fermions coupled to external gauge fields, the axial anomaly has a simple physical interpretation in terms of level shifting at the top of the Dirac sea. We apply this formalism to lattice QED in 1 + 1 and 3 + 1 dimensions, in order to study how the lattice regulation and small fermion mass affect the picture. For a simple choice of the E and B fields, it is possible to accurately follow the time evolution of the (lattice) Dirac sea of Wilson fermions. We find that the Wilson r term plays a role, with respect to the anomaly, which is closely analogous to point-splitting in the continuum. This role is jeopardized whenever the Wilson mass scale r/ a is comparable to other physical mass scales in the problem, as is the case, for example, in strong coupling calculations. Remarkably, we find that hadronic scales of only a few lattice spacings are probably sufficient to guarantee the proper anomaly structure.

Quasiclassical description of the vacuum instability in an external non-Abelian gauge field

Quasiclassical description of the vacuum instability in an external non-Abelian gauge field

Spontaneous symmetry breaking in Kaluza-Klein theories

We study the bosonic spectrum of Kaluza-Klein theories by considering the symmetries of the vacuum. We find that the introduction of external gauge fields with non-vanishing vacuum expectation values affects the massless vectors and may break isometries of the internal space making the corresponding gauge vectors massive.

Six-dimensional supersymmetric Yang-Mills theory is not finite

We find that the transition amplitudes with three external gauge fields and four external fermions are not finite in the six-dimensional supersymmetric Yang-Mills model.

Radiative correction to the energy of a fermion in an external gauge field

The first radiative correction in g2 to the energy of the ground state of a fermion in a constant uniform gauge (for the SU(2) group) field of magnetic type is calculated. The expression obtained contains an indication of instability of the ground state.

Colored, spinning classical particle in an external non-abelian gauge field

We derive classical non-relativistic equations of motion for a colored, spinning point-like particle in an external SU(2) gauge field from Dirac equation. We find that in addition to the classical spin and color spin vector, S, I, it is necessary to introduce a new classical dynamical variable [ J ab ], a, b = 1, 2, 3, describing a mixing of the spin and color. The constraint relations between [ J ab ], S, I are also found.

Rarita-Schwinger field in non-abelian Klein-Kaluza theories

The author deals with 3/2-spinor fields in the framework of the non-abelian Klein-Kaluza theory. He introduces a dimensional reduction procedure for a 3/2-spinor field and a generalisation of the minimal coupling scheme. He gets dipole electric moments for a 3/2-spin particle of value 10-31 cm and PC breaking for a gauge group G with odd parameters. Reflections in higher (additional) dimensions were proposed as a conjugation of 'colour' charges connected with Yang-Mills fields. His approach avoids the Velo-Zwanziger paradox (acausal propagation in an external gauge field).

Path integral in superspace for a relativistic spinor particle in an external gauge field

Path integral in superspace for a relativistic spinor particle in an external gauge field