PlanetPhysics/Axiomatics and Categorical Foundations of Mathematical Physics

Axiomatics and Categorical Foundations of Mathematical Physics

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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 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 -algebras and groupoid convolution -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

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References

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