Quantum physics

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Feynman Diagram for Gluon Radiation


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Bibliography

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  • ... more to come
  • [12] Brown R (2004) Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems. In: Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, September 23-28, 2004, Fields Institute Communications 43:101-130.
  • [13] Brown R, Hardie K A, Kamps K H, and Porter T (2002) A homotopy double groupoid of a Hausdorff space. Theory and Applications of Categories 10:71-93.
  • [14] Georgescu G, and Popescu D (1968) On Algebraic Categories. Revue Roumaine de Mathematiques Pures et Appliquées 13:337-342.
  • [15] Georgescu G, and Vraciu C (1970) On the Characterization of Łukasiewicz Algebras. J. Algebra, 16 (4):486-495.
  • [16] Georgescu G (2006) N-valued Logics and Łukasiewicz-Moisil Algebras. Axiomathes 16 (1-2): 123-136.
  • [17] Landsman N P (1998) Mathematical topics between classical and quantum mechanics. Springer Verlag, New York.

Quantum Logics

Notation Table

Polish- or Łukasiewicz's notation for logic

Concept Conventional
notation
Polish
notation
Polish / English
word
w:Negation ¬ϕ negation (No)}
Conjunction ϕψ Kφψ conjunction
w:Disjunction ϕψ Aφψ alternate OR=disjunction
w:Material conditional ϕψ Cφψ implication
w:Biconditional ϕψ Eφψ equivalence'
w:Falsum O False value
w:Sheffer stroke ϕψ Dφψ Sheffer stroke
Possibility ϕ contingent
Necessity ϕ Necessary condition
w:Universal quantifier Πpφ kwantyfikator ogólny ANY:

For all p, \phi|Universal quantifier

Existential quantifier pϕ Σpφ Exists
  • Note that the quantifiers ranged over propositional values in Łukasiewicz's work on many-valued logics.

See also