Abstracts, files, and links supplied by the speakers

Jens Bolte, Trace Formulas

Gerald Dunne, Mass Dependence of Instanton Determinant in QCD (Part I)

Stephen Fulling:

  1. Some Mathematical and Physical Background
  2. The Hamilton-Jacobi Equation, Semiclassical Asymptotics, and Stationary Phase
  3. What Is Vacuum Energy, that Mathematicians Should Be Mindful of It?

Kishore Kapale, Topics in Statistical Mechanics and Quantum Optics

Peter Kuchment, A Brief Survey on Quantum Graphs and Their Applications

Robert Littlejohn, Quantum Normal Forms, Moyal Star Product and Torus Quantization: We develop a normal form transformation for complete sets of commuting operators that maps the operators by unitary conjugation into functions of the harmonic oscillators in the various degrees of freedom. The transformation takes place at the level of Weyl symbols, treated as formal power series in hbar, and uses the Moyal star product as a basic building block. One of the operators (the Hamiltonian) is required to have a generic, stable fixed point in phase space. Diagrammatic techniques are developed for representing the higher order tensorial objects that are generated by the Moyal series. Once the normal form is achieved, the torus (or EBK) quantization rule follows immediately, including higher order corrections. These raise some interesting issues in differential geometry.

Kimball Milton, Surface Divergences and Boundary Energies in the Casimir Effect

Hyunsoo Min, Mass Dependence of Instanton Determinant in QCD (Part II)

Antonello Scardicchio: See the paper on the background reading page.

Christian Schubert, Worldline instantons and WKB (joint work with G.V. Dunne): One-loop effective actions in quantum field theory can be represented in terms of relativistic particle path integrals. For the constant field case, Affleck et al. have shown that Schwinger's famous formula for the imaginary part of the effective action can be obtained from the corresponding path integral by expanding it around an instanton type solution. We generalize their approach to a large class of external field configurations and show how to construct the appropriate instanton solutions. We present explicit results for the imaginary part of the effective action for some cases, and compare with known results from WKB.

Last modified Thu 14 Jan 2010