Gauge Field Theory in Natural Geometric Language A revisitation of mathematical notions of quantum physics

Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.

Daniel Canarutto is a mathematical physicist interested in the clarification of mathematical notions of fundamental physics, using natural differential geometry as the main tool. His earlier work includes results about the geometry of spacetime singularities. Since 1993 he has focused on basic notions underlying quantum physics, revisiting several aspects within partly original approaches to spinor geometry, distributional bundles and other geometry-related topics.