Gauge Field Theory Without Groups

ISBN : 9780198861492

Daniel Canarutto
330 Pages
156 x 234 mm
Pub date
Oct 2020
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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.


1 Bundle prolongations and connections
2 Special algebraic notions
3 Spinors and Minkowski space
4 Spinor bundles and spacetime geometry
5 Classical gauge field theory
6 Gauge field theory and gravitation
7 Optical geometry
8 Electroweak geometry and fields
9 First-order theory of fields with arbitrary spin
10 Infinitesimal deformations of ECD fields
11 Generalised maps
12 Special generalised densities on Minkowski spacetime
13 Multi-particle spaces
14 Bundles of quantum states
15 Quantum bundles
16 Quantum fields
17 Detectors
18 Free quantum fields
19 Electroweak extensions
20 Basic notions in particle physics
21 Scattering matrix computations
22 Quantum electrodynamics
23 On gauge freedom and interactions

About the author: 

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.

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