The Classical Theory of Fields (Book): Difference between revisions
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| title = === Foundations of Differential Geometry === | |||
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| desc = Gauge Fields and Cartan-Ehresmann Connections by Robert Hermann. | | desc = Gauge Fields and Cartan-Ehresmann Connections by Robert Hermann. | ||
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| link = Gauge Field Theory and Complex Geometry (Book) | |||
| title = === Gauge Field Theory and Complex Geometry === | |||
| desc = Gauge Field Theory and Complex Geometry by Yuri Manin. | |||
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Revision as of 23:18, 2 February 2024
| Fields | |
| |
| Information | |
|---|---|
| Author | Lev Landau |
| Language | English |
| Series | Course of Theoretical Physics |
| Publisher | Butterworth Heinemann |
| Publication Date | 1975 |
| Pages | 402 |
| ISBN-13 | 978-0-7506-2768-9 |
The Classical Theory of Fields represents another major challenge for the mathematical and physical maturity of the reader. Understanding the application of relativity requires setting aside the Galilean idea of time and assuming the formalism of change of basis from linear algebra to describe basic physical quantities such as vector and tensor fields in space-time. Least action functions similarly to mechanics, action being measured by integrals along trajectories, but differs in there being no absolute time to integrate against. Due to this least action approach, Electromagnetism is described starting from a four-vector potential rather than the usual Electric and Magnetic fields as they do not exist geometrically on space-time (and because the potential more simply integrates with the action). Culminating in General relativity, physics in curved space is described with covariant derivatives, christoffel symbols, parallel transport, and phenomena such as gravitational waves and black holes are derived. This text marks another nail in the coffin of non-geometric physics and strongly urges the reader to pursue differential geometry, and aids in that process by applying indicial tensor calculus.
Applications
Lectures on Differential Geometry
Lectures on Differential Geometry by Shlomo Sternberg.
Differential Forms in Algebraic Topology
Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu.
Curvature in Mathematics and Physics
Curvature in Mathematics and Physics by Shlomo Sternberg.
Geometry of Yang-Mills Fields
Geometry of Yang-Mills Fields by Michael Atiyah.
Spinors and Space-Time
Spinors and Space-Time by Roger Penrose and Wolfgang Rindler.
Characteristic Classes
Characteristic Classes by John Milnor and James Stasheff.
K Theory
K Theory by Michael Atiyah.
Foundations of Differential Geometry
Foundations of Differential Geometry by Shoshichi Kobayashi and Katsumi Nomizu.
Spin Geometry
Spin Geometry by H. Blaine Lawson jr. and Marie-Louise Michelsohn.
Gauge Fields and Cartan-Ehresmann Connections
Gauge Fields and Cartan-Ehresmann Connections by Robert Hermann.
Gauge Field Theory and Complex Geometry
Gauge Field Theory and Complex Geometry by Yuri Manin.
Einstein Manifolds
Einstein Manifolds by Arthur Besse.