A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional Example

We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion.Comment: 10 pages, RevTeX, 2 figures composed from 4 .eps files; v2: fixed minor errors, added reference; v3: corrected reference added in v

Soliton Models for the Nucleon and Predictions for the Nucleon Spin Structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave--functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.Comment: 12 pages, Lectures presented at the Advanced Study Institute Symmetry and Spin, Prague, 2001, to appear in the proceedings. References correcte

THE NATURE OF TURBULENT KINETIC ENERGY IN A DEEP AND NARROW VALLEY UNDER CONVECTIVE (?) CONDITIONS

This contribution investigates the nature of turbulent kinetic energy (TKE) in a steep and narrow Alpine valley under fair-weather summertime conditions. The Riviera Valley in southern Switzerland has been chosen for a detailed case study, in which the evaluation of aircraft data (obtained from the MAP-Riviera field campaign) is combined with the application of high-resolution (350 m) large-eddy simulations using the model ARPS. The simulations verify what has already been observed on the basis of measurement data: TKE profiles scale surprisingly well if the convective velocity scale w٭ is obtained from the sun-exposed eastern slope rather than from the surface directly underneath the profiles considered. ARPS is then used to evaluate the TKE-budget equation, showing that, despite sunny conditions, wind shear is the dominant production mechanism. Therefore, the surface heat fluxes (and thus w٭) on the eastern slope do not determine the TKE evolution directly but rather, as we believe, indirectly via the interaction of thermally-driven crossvalley and along-valley flow. Excellent correlations between w2٭ and the up-valley wind speed solidify this hypothesis

Heavy Fermion Stabilization of Solitons in 1+1 Dimensions

We find static solitons stabilized by quantum corrections in a (1+1)-dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional.Comment: 27 papes Latex, equation labels corrected, version to be published in Nucl. Phys.

Heavy Fermion Quantum Effects in SU(2)_L Gauge Theory

We explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable.Comment: 30 pages LaTeX, 3 eps-figure

Searching for Quantum Solitons in a 3+1 Dimensional Chiral Yukawa Model

We search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model.Comment: 27 pp., 7 EPS files; email correspondence to [email protected]

Fractional and Integer Charges from Levinson's Theorem

We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1+1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions.Comment: 16 pages, uses RevTex, 1 figure; v2: minor correction

Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir Problem

The Casimir problem is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions. In reality, however, no interaction is strong enough to enforce a boundary condition on all frequencies of a fluctuating field. We construct a more physical model of the situation by coupling the fluctuating field to a smooth background potential that implements the boundary condition in a certain limit. To study this problem, we develop general new methods to compute renormalized one--loop quantum energies and energy densities. We use analytic properties of scattering data to compute Green's functions in time--independent background fields at imaginary momenta. Our calculational method is particularly useful for numerical studies of singular limits because it avoids terms that oscillate or require cancellation of exponentially growing and decaying factors. To renormalize, we identify potentially divergent contributions to the Casimir energy with low orders in the Born series to the Green's function. We subtract these contributions and add back the corresponding Feynman diagrams, which we combine with counterterms fixed by imposing standard renormalization conditions on low--order Green's functions. The resulting Casimir energy and energy density are finite functionals for smooth background potentials. In general, however, the Casimir energy diverges in the boundary condition limit. This divergence is real and reflects the infinite energy needed to constrain a fluctuating field on all energy scales; renormalizable quantum field theories have no place for ad hoc surface counterterms. We apply our methods to simple examples to illustrate cases where these subtleties invalidate the conclusions of the boundary condition approach.Comment: 36pages, Latex, 20 eps files. included via epsfi