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The Classical Theory of Fields (Book): Difference between revisions
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The final basic text on gauge theory here, by [[Robert Hermann]], is rather special because he was the person to originally point out that the underlying geometry of the forces of the standard model was Gauge theory. He was often not credited, but those in the know knew it was him such as Singer or Gilkey. His book also adds substance, because it is the only one here that directly discusses models of physical phenomena and includes his personal thoughts on the direction of the field. All of his books are a must-read, for those pursuing research in an independent manner following our culture here. Manin's book on the other hand, represents his standing as one of the last Russian mathematical physicists deeply involved in both subjects. It takes the construction of instantons, the YM to Twistor conversion to a higher level (which is the complex geometry part), and the supermanifold enhancement of YM. We believe supersymmetry is heavily misinterpreted/mis-instantiated in physics, and hopefully you will see here that the direction mathematics takes it is different and useful. | The final basic text on gauge theory here, by [[Robert Hermann]], is rather special because he was the person to originally point out that the underlying geometry of the forces of the standard model was Gauge theory. He was often not credited, but those in the know knew it was him such as Singer or Gilkey. His book also adds substance, because it is the only one here that directly discusses models of physical phenomena and includes his personal thoughts on the direction of the field. All of his books are a must-read, for those pursuing research in an independent manner following our culture here. Manin's book on the other hand, represents his standing as one of the last Russian mathematical physicists deeply involved in both subjects. It takes the construction of instantons, the YM to Twistor conversion to a higher level (which is the complex geometry part), and the supermanifold enhancement of YM. We believe supersymmetry is heavily misinterpreted/mis-instantiated in physics, and hopefully you will see here that the direction mathematics takes it is different and useful. | ||
The most difficult book here by far is Besse's, as it assumes dexterity with nearly all of the above constructions and geometry. In short, an Einstein structure is the GR analog of an instanton, and this book | The most difficult book here by far is Besse's, as it assumes dexterity with nearly all of the above constructions and geometry. In short, an Einstein structure is the GR analog of an instanton, and this book constructs some and describes their topological consequences. | ||
=== Applications === | === Applications === | ||