Geometry Articles



The Geometry of Mathematical Quantum Field Theory

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…

When Simple Geometry Unveils Deep Math

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

How to Self Study Geometry: Pure Geometry

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…

Higher Prequantum Geometry V: The Local Observables - Lie Theoretically

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

Higher Prequantum Geometry IV: The Covariant Phase Space - Transgressively

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

Higher Prequantum Geometry III: The Global Action Functional - Cohomologically

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

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

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

Higher Prequantum Geometry I: The Need for Prequantum Geometry

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