Scaling approach for the time-dependent Kondo model

We present a new nonperturbative method to deal with the time-dependent quantum many-body problem, which is an extension of Wegner's flow equations to time-dependent Hamiltonians. The formalism provides a scaling procedure for the set of time-dependent interaction constants. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale $\tau$. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value

Pair creation and axial anomaly in light-cone QED2QED_2

The 1+1 dimensional massive Dirac equation is solved exactly in light-cone coordinates for $x^+ > 0$ and $x^- > -L$, in the presence of an arbitrary $x^+$ dependent electric field. Our solution resolves the ambiguity at $p^+ = 0$. We also obtain the one loop rate for pair production for a positive electric field, compute the expectation values of the vector and axial vector currents, and recover the well known anomaly $e^2 E/\pi$ in the divergence of the latter. A final intriguing result is that the theory seems to exhibit a phase transition in the limit of infinite $L$.Comment: 33 pages, 2 figures, LaTeX 2 epsilon, revised for publicatio

Ribbons Around Mexican Hats

We analyze quasi-topological solitons winding around a mexican-hat potential in two space-time dimensions. They are prototypes for a large number of physical excitations, including Skyrmions of the Higgs sector of the standard electroweak model, magnetic bubbles in thin ferromagnetic films, and strings in certain non-trivial backgrounds. We present explicit solutions, derive the conditions for classical stability, and show that contrary to the naive expectation these can be satisfied in the weak-coupling limit. In this limit we can calculate the soliton properties reliably, and estimate their lifetime semiclassically. We explain why gauge interactions destabilize these solitons, unless the scalar sector is extended.Comment: 12p. Latex , Ecole Polytechnique preprint A295.02.94 and Crete preprint 94-1

Maxwell--Chern-Simons gauged non-relativistic O(3) model with self-dual vortices

A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the ungauged model, these vortices are shown to exhibit Hall behaviour in their dynamics.Comment: 12 pages, LateX, to appear in Mod. Phys. Lett. 199

Schwinger's Propagator Is Only A Green's Function

Schwinger used an analytic continuation of the effective action to correctly compute the particle production rate per unit volume for QED in a uniform electric field. However, if one simply evaluates the one loop expectation value of the current operator using his propagator, the result is zero! We analyze this curious fact from the context of a canonical formalism of operators and states. The explanation turns out to be that Schwinger's propagator is not actually the expectation value of the time-ordered product of field operators in the presence of a time-independent state, although it is of course a Green's function. We compute the true propagator in the presence of a state which is empty at $x_+ = 0$ where $x_+ \equiv (x^0+x^3)/\sqrt{2}$ is the lightcone evolution parameter. Our result can be generalized to electric fields which depend arbitrarily on $x_+$.Comment: 18 pages, LaTeX 2 epsilo

Gravitating defects of codimension-two

Thin gravitating defects with conical singularities in higher codimensions and with generalized Israel matching conditions are known to be inconsistent for generic energy-momentum. A way to remove this inconsistency is proposed and is realized for an axially symmetric gravitating codimension-two defect in six dimensional Einstein gravity. By varying with respect to the brane embedding fields, alternative matching conditions are derived, which are generalizations of the Nambu-Goto equations of motion of the defect, consistent with bulk gravity. For a maximally symmetric defect the standard picture is recovered. The four-dimensional perfect fluid cosmology coincides with conventional FRW in the case of radiation, but for dust it has rho^{4/3} instead of rho. A four-dimensional black hole solution is presented having the Schwarzschild form with a short-distance correction r^{-2}.Comment: Minor changes, to appear in Classical and Quantum Gravit