Sheafification – The optimal path to mathematical mastery

Summary

Steven Weinberg – The Quantum Theory of Fields Once again, there are three books, so we will summarize them generally and then per-volume below. Weinberg takes a middle road between directly showing how practical calculations are done and the geometric picture. The core of this compromise is to elevate the representation theoretic Wigner classification of particles in volume 1 to the beginning, and to make it as clear as possible what quantum field theory is about and how to make sense of it. Landau 4 on quantum electrodynamics thus makes a good companion, focusing on the special case of electrodynamics but being compatible with the formalism here. You will come out of volume 1 as an expert on the fundamentals of QFT, volume 2 bridges to the gauge geometry central to much of this list, and volume three, supersymmetry. See below for more: Table of Contents Volume 1: Foundations This volume contains the basic tools to do quantum field theory, coming from quantum mechanics, which we would like to expound upon in another blog post. These tools have produced the most accurate scientific predictions in history, due to the relative accessibility of scattering experiments and their direct connection to the theoretical formalism and relativistically invariant particle Hilbert spaces. Volume 2: Modern Applications Beginning in a coordinatized version of the gauge theory from Atiyah Yang-Mills, analogies between the change of gauge to coordinate changes in general relativity are noted and immediately the many techniques in approaching the quantization of these force fields are listed. A focus on the physical content of the mathematics follows, such as the important applications to Electroweak symmetry breaking and instantons. Volume 3: Supersymmetry Supersymmetry has garnered a peculiar reputation as “not being physics.” It is the point of view of the authors of the fast track, who fundamentally care about physical reality, that supersymmetry just has not been properly underst...