physicslib4 reference manual🔗

This manual describes how physicslib4 encodes the mathematics of algebraic quantum field theory: which definitions the library makes, why they take the form they do, which theorems it proves, and where they live. It has one chapter per section of Chapter 10 of the blueprint. The tutorial introduces the subject; the API documentation lists every declaration. The library's conventions and design decisions are stated once, in the chapter Conventions and design decisions, and the standard facts it does not prove are listed in the appendix.

Contents

  1. 1. The GNS construction
  2. 2. Bounded spectral theory
  3. 3. Unbounded operators and their spectral theorem
  4. 4. Stone's theorem
  5. 5. Spacetime and geometry
  6. 6. The Haag–Kastler axioms in Minkowski spacetime
  7. 7. The axioms in curved spacetime and general covariance
  8. 8. Conventions and design decisions
  9. 9. Appendix: what the library does not prove