Scattering matrix in external field problems

Abstract

We discuss several aspects of second quantized scattering operators $\hat{S}$ for fermions in external time dependent fields. We derive our results on a general, abstract level having in mind as a main application potentials of the Yang--Mills type and in various dimensions. We present a new and powerful method for proving existence of $\hat{S}$ which is also applicable to other situations like external gravitational fields. We also give two complementary derivations of the change of phase of the scattering matrix under generalized gauge transformations which can be used whenever our method of proving existence of $\hat{S}$ applies. The first is based on a causality argument i.e.\ $\hat{S}$ (including phase) is determined from a time evolution, and the second exploits the geometry of certain infinite-dimensional group extensions associated with the second quantization of 1-particle operators. As a special case we obtain a Hamiltonian derivation of the the axial Fermion-Yang-Mills anomaly and the Schwinger terms related to it via the descent equations, which is on the same footing and traces them back to a common root.

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References in corpus (9)

• Fermion Current Algebras and Schwinger Terms in 3+1 Dimensions
• (3+1)-Dimensional Schwinger Terms and Non-commutative Geometry
• Descent equations of Yang--Mills anomalies in noncommutative geometry
• QED in external fields from the spin representation
• Cocycles for Boson and Fermion Bogoliubov Transformations
• Hilbert space cocycles as representations of $(3+1)-$ D current algebras
• Non--commutative Integration Calculus
• Regularization of current algebra
• Schwinger terms, gerbes, and operator residues

Cited by in corpus (9)

• Time Evolution of the External Field Problem in QED
• The Phase of the Scattering Matrix
• Dirac Equation with External Potential and Initial Data on Cauchy Surfaces
• Dirac field on Moyal-Minkowski spacetime and non-commutative potential scattering
• Quantum fields with classical interactions
• Vacuum polarization and the geometric phase: Gauge invariance
• Quantum Gauge Theories and Noncommutative Geometry
• The phase of the scattering operator from the geometry of certain infinite-dimensional groups
• External Field QED on Cauchy Surfaces