Anton Z. Capri

Propagation of interacting fields

Abstract The spin one theory of Takahashi and Palmer [4] leads to acausal propagation when minimally coupled to an electromagnetic field. The addition of an anomalous magnetic moment (Pauli term) allows one to recover causal propagation. In the case of the Rarita-Schwinger spin 3 2 theory it is impossible to obtain causal propagation even when all possible Pauli terms are included. Coupling of a massive spin 1 2 and massive spin 1 theory leads to causal propagation for all nonderivative vector and tensor couplings, pseudo scalar and pseudo vector couplings.

Properties of the Schwinger model

We present all the Wightman functions for an explicit operator solution of the Schwinger model. To understand these better, we study the algebra of fields of this model, representations of this algebra as well as the Hamiltonian. The latter turns out to elucidate the ‘‘confinement’’ of the fermion field. In addition we comment on the renormalization of the theory as well as on the analyticity of the amplitudes in terms of the coupling constant.

Fock space construction of the massless dipole field

Abstract We construct the Fock space representation of the free massless scalar dipole field in terms of creation and annihilation operators for the eigenvectors of the momentum operator. The Poincare group is implemented unitarily only on a subspace of the full (positive metric) Hilbert space. The subspace possesses a hermitean, local, irreducible scalar field constructed out of the (non-hermitean) dipole field. Thus this subspace is a perfect candidate for a physical subspace of observable particles. We show that this possibility is however excluded by the fact that these particles interact with an external c-number source in a manner that violates unitarity. We illustrate our construction by applying it to the linearized Higgs model with external c-number source and examine the (non-trivial) dynamics of the dipole degrees of freedom in this case. An explicit separation of the physical degrees of freedom from the unphysical ones is presented for this interacting model.

A mechanical model with constraints

We analyze a dynamical system with a finite number of degrees of freedom. A complete analysis is presented both for first class constraints as well as for second class constraints. The results are applicable to Yang–Mills fields as well as higher spin fields.

Eigenmodes for an elastic halfspace surrounding a semi-rigid cylinder

Abstract The elastodynamics of a halfspace with a cylindrical hole belongs to a class of problems which involve solving the elastic wave equation in a geometry that is bounded by nonparallel surfaces. Integral transform techniques are not very suitable for the solution of such problems because the transform approach yields solutions in terms of wavefronts (or rays). For a nonparallel geometry one may need a large collection of such terms and this may be an inconvenient description. So, we have taken an approach to construct the eigenmodes (normal modes) for this geometry for a given set of boundary conditions. A set of linearly independent solutions, without any reference to sources or receivers, is developed and completeness of this set is verified explicitly. Using this complete set of eigenmodes the displacement field for any source problem in this geometry can be expressed following standard mathematical procedures.