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qtf_geometry

The Geometry of Mathematical Quantum Field Theory

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This is the first chapter in a series on Mathematical Quantum Field Theory.The next chapter is 2. Spacetime. 1. Geometry The geometry of physics…
geometrysimple

When Simple Geometry Unveils Deep Math

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Introduction It is a remarkable fact that consideration of very elementary concepts in geometry often leads quickly into deep and unexpected mathematical…
geometry1

How to Self Study Geometry: Pure Geometry

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Geometry is one of the oldest parts of mathematics. It has been studied and advanced by the greatest minds humankind has to offer. It has been described…
prequantumgeometry5

Higher Prequantum Geometry V: The Local Observables - Lie Theoretically

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 This article discusses how from the previous considerations naturally follow the concepts of local observables of local field theories and…
prequantumgeometry4

Higher Prequantum Geometry IV: The Covariant Phase Space - Transgressively

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  The Euler-Lagrange ##p##-gerbes discussed in the previous article are singled out as being exactly the right coherent refinement…
prequantumgeometry3

Higher Prequantum Geometry III: The Global Action Functional - Cohomologically

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  The previous article ended with the concept of classical locally variational field theories, of which a class of examples are…
prequantumgeometry2

Higher Prequantum Geometry II: The Principle of Extremal Action - Comonadically

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  The previous article motivated the importance of considering "pre-quantum field theory" in between classical and quantum field…
prequantumgeometry

Higher Prequantum Geometry I: The Need for Prequantum Geometry

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 Before proceeding with discussion of the super p-brane sigma models, whose emergence from the superpoint I discussed in the previous article,…