PlanetPhysics/Axiomatics and Categorical Foundations of Mathematical Physics

Axiomatics and Categorical Foundations of Mathematical Physics
This is a contributed new topic on the mathematical foundations of theoretical physics and quantum theories.


 * 1) Axiomatic foundations of quantum field theories
 * 2) quantum logics and logic algebras: Post and $$MV$$ logics
 * 3) Index of Quantum Algebraic Topology #adjointness, equivalence, isomorphism at the foundations of categorical physics #category theory in quantum physics and general relativity #Categories of quantum logic algebras
 * 4) functor categories and super-categories #index of category theory #indexes of category
 * 5) classification of $$C^*$$-algebras and groupoid convolution $$C^*$$-algebras
 * 6) Quantum topoi and quantum logic extended-toposes
 * 7) non-Abelian structures and gauge theories
 * 8) Non-Abelian Quantum Algebraic Topology and AQFT #Classical and categorical Galois theories of quantum groups and quantum groupoids
 * 9) Theory of quantum computation: quantum logics, quantum automata and quantum computation
 * 10) Measure theory and probability in quantum statistical mechanics #quantum symmetries and quantum groupoid representation theory
 * 11) noncommutative geometry, SUSY and axiomatic quantum gravity (AQG)

Literature references for mathematical physics foundations: axiomatics and categories