Ola Tornkvist

Vortex Dynamics in Dissipative Systems

We derive the exact equation of motion for a vortex in twoand three-dimensional nonrelat systems governed by the Ginzburg-Landau equation with complex coefficients. The velocity is in terms of local gradients of the magnitude and phase of the complex field and is exact al arbitrarily small intervortex distances. The results for vortices in a superfluid or a superconduc recovered. [pub S0031-9007(97)02621-5]

Electroweak origin of cosmological magnetic fields

Magnetic fields may have been generated in the electroweak phase transition through spontaneous symmetry breaking or through the subsequent dynamical evolution of semiclassical field configurations. Here I demonstrate explicitly how magnetic fields emerge spontaneously in the phase transition also when no gradients of the Higgs field are present. Using a simple model, I show that no magnetic fields are generated, at least initially, from classical two-bubble collisions in a first-order phase transition. An improved gaugeinvariant definition of the electromagnetic field is advocated which is more appropriate in the sense that it never allows electrically neutral fields to serve as sources for the electromagnetic field. In particular, semiclassical configurations of the Z field alone do not generate magnetic fields. The possible generation of magnetic fields in the decay of unstable Z-strings is discussed.

ℤ2 as the topological origin of B + L violation in the hot electroweak theory

Abstract The space of static finite-energy configurations in the electroweak theory admits a ℤ 2 2 topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon- and lepton-number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, as well as an infinite surface of their equivalents, have half-integer Chern—Simons number and mediate B + L violating processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the S * new sphaleron, are topologically equivalent to the vacuum and are irrelevant for B + L violation. Electroweak string configurations comprise continuous families of sphaleron equivalents as well as configurations equivalent to the vacuum. We discuss the possible formation of B + L violating quark-lepton condensates in the symmetric high-temperature phase of the electroweak theory.

Towards a string formulation of vortex dynamics

We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom.We derive an exact equation of motion for a non-relativistic vortex in twoand three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem of reducing the field dynamics to a closed dynamical system with non-locally interacting strings as the fundamental degrees of freedom. ∗Talk presented by O.T. at the International Workshop on Solitons, their Properties, Dynamics, Interactions, and Applications in Kingston, Ontario, Canada, 20-26 July 1997. To appear in the proceedings. ‡Electronic address: schroder@nbi.dk §Electronic address: O.Tornkvist@damtp.cam.ac.uk ¶Present address.

THE ORIGIN OF COSMIC MAGNETIC FIELDS

In this talk, I review a number of particle-physics models that lead to the creation of magnetic fields in the early universe and address the complex problem of evolving such primordial magnetic fields into the fields observed today. Implications for future observations of the Cosmic Microwave Background (CMB) are discussed. Focussing on first-order phase transitions in the early universe, I describe how magnetic fields arise in the collision of expanding true-vacuum bubbles both in Abelian and non-Abelian gauge theories.

COSMIC MAGNETIC FIELDS FROM PARTICLE PHYSICS

I review a number of particle-physics models that lead to the creation of magnetic fields in the early universe and address the complex problem of evolving such primordial magnetic fields into the fields observed today. Implications for future observations of the Cosmic Microwave Background (CMB) are briefly discussed.I review a number of particle-physics models that lead to the creation of magnetic fields in the early universe and address the complex problem of evolving such primordial magnetic fields into the fields observed today. Implications for future observations of the Cosmic Microwave Background (CMB) are briefly discussed.

Magnetic fields from the electroweak phase transition

I review some of the mechanisms through which primordial magnetic fields may be created in the electroweak phase transition. I show that no magnetic fields are produced initially from two-bubble collisions in a first-order transition. The initial field produced in a three-bubble collision is computed. The evolution of fields at later times is discussed.I review some of the mechanisms through which primordial magnetic fields may be created in the electroweak phase transition. I show that no magnetic fields are produced initially from two-bubble collisions in a first-order transition. The initial field produced in a three-bubble collision is computed. The evolution of fields at later times is discussed.