Some Related Work

Other axiomatic approaches to the foundations of quantum mechanics

Pioneers in this area were Garreth Birkhoff & John von Neumann, George Mackey, Joseph Jauch & Constantin Piron, Dave Foulis & Charles Randall and Gunther Ludwig. Survey's are:

The founding paper was:

  • Birkhoff, G. and von Neumann, J. (1936), The Logic of Quantum Mechanics, Annals of Mathematics 37, 823—843.

There are also the tracts:

  • Mackey, G.W. (1963), Mathematical Foundations of Quantum Mechanics, W.A. Benjamin Inc.
  • Piron, C. (1976), Foundations of Quantum Physics, W.A. Benjamin Inc.
  • Ludwig, G. (1985; 1987), An Axiomatic Basis of Quantum Mechanics: 1. Derivation of Hilbert Space; 2. Quantum Mechanics and Macrosystems, Springer-Verlag.

Some current developments are:

Categories in logic and foundations of computing

A Milestone:

Formally, this logical development stands orthogonal to Birkhoff/von Neumann quantum logic. It is rather this logic and not Birkhoff/von Neumann quantum logic which provides the logical foundation for the Monoidal approach, making the ability to copy and delete premisses explicit. Although not yet as articulated and exploited as Girrard's Linear Logic, one could argue that Linear Logic was already present in Jim Lambek's earlier work on mathematical linguistics (1956) and categorical logic (1970's). The categorical semantics of Linear Logic based on Mike Barr's *-autonomous categories is in:

More recent computer science motivated developments are:

Earlier work on categories in foundations of physics

Categories in mathematical physics

General category theory resources

General physics resources

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