N. J. Papastamatiou

The boson transformation and the vortex solutions

Abstract The boson transformation, which allows the construction of spontaneously broken solutions with space and/or time-dependent vacuum directly from the translationally invariant ones, is examined in the context of the Higgs mechanism. Both the Lorentz and the radiation gauge are treated in detail. The classical vortex solution is derived by fully quantum field theoretical considerations. The general form of the vortex solution is presented, and various special cases of interest are examined in detail.

The Goldstone theorem and dynamical rearrangement of symmetry in the path- integral formalism

Abstract The spontaneous breakdown of symmetry is investigated in the path-integral formalism. The generating functional is modified by the addition of a limiting “ϵ term” which fixes the direction of the breaking. The method is illustrated by means of several models with Abelian symmetries. The Goldstone theorem is a result of Ward-Takahashi identities in which the ϵ term plays a decisive role. The problem of how the original symmetry transformation of the Heisenberg fields manifests itself at the level of observable (physical) particles, expressed in terms of the in-field operators φ in ( χ ), is investigated. It is proved that, if spontaneous breakdown is present, the in-field transformation φ in ( χ ) → φ in ( χ ) + α ( χ ), with α (χ) satisfying the same field equation as φ in ( χ ) (Boson transformation), is an invariant transformation (i.e. leaves the equation of motion of the Heisenberg fields unchanged). It is also found that, when spontaneous breaking occurs, the invariant transformations of the Heisenberg and in-fields are different (dynamical rearrangement of symmetry). The form of the invariant in-field transformation is established for several models.

Dynamical rearrangement in the Anderson-Higgs-Kibble mechanism☆

The Anderson-Higgs-Kibble mechanism is investigated by functional methods in the Lorentz gauge, with particular emphasis on the particle structure. We find that a massless Goldstone boson and a massless ghost particle are present besides the massive vector meson and other massive particles. The two massless particles do not contribute to matrix elements of the S-matrix or any gauge invariant quantity, because their effects compensate each other, but their presence is essential as agents of the symmetry transformations. The modifications when the Coulomb gauge is employed are also discussed.

The formulation of spontaneous breakdown in the path-integral method☆

Abstract We examine the problem of formulating spontaneous breakdown of symmetries in the path-integral framework; since different solutions of the field equations correspond to different boundary conditions, the possibility of different boundary conditions must be incorporated in the generating functional itself. We propose a modification of the generating functional that provides the required flexibility that can lead to different solutions. We apply our formalism to a model of scalar complex fields with invariance under phase transformations of the first kind and derive Ward-Takahashi identities and the Goldstone theorem.

Comments on the perturbed sine–Gordon equation

We examine the sine–Gordon equation with a perturbation λΔV. We derive necessary conditions on ΔV such that the perturbed equation has solutions with finite energy, analytic in λ, and which reduce to the static soliton when the perturbation is removed (λ→0). Several examples illustrating these conditions are presented.