The Quantum Theory of Fields Volume

Quantum electrodynamics (QED) is the branch of relativistic quantum field theory that deals specifically with the interactions between charged particles. It is widely used to solve problems in many areas of physics, such as elementary particles, atomic and molecular systems, and solid state physics.

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. It is shown that these algebras have natural integral forms that can be specialized at roots of 1 and yield new objects, which include quantum versions of the semi-simple groups over fields of positive characteristic.

Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.