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Mathematics portal

• • Quantum physics, Wikiversity projects on the interpretation of quantum theories:
    • Département:Mécanique quantique
      • Département:Logique quantique
    • Quantum computing
    • Quantum Logics
    • w.Quantum Logics
    • Quantum physics at Wikipedia

Feynman Diagram for Gluon Radiation

External links

• Quantum Physics Collaboration
• Quanta- a new OJS journal
• PlanetPhysics.org' MediaWiki version 1.17 Quantum Book Projects
  • Applied Quantum Systems and Quantum Theory Foundations--A PlanetPhysics.org collaboration
• Q-logics of Quantum Automata
• Quantum Algebra Textbook:"Quantum Algebra, Quantum Computers and Symmetries", 2011. 727 pages, free downloads, OpenSource, 27Mb PDF file
• Łukasiewicz, or Polish, Notation

Bibliography

• ... 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

• The table below shows the core of w:Jan Łukasiewicz's notation for w:sentential logic, or Propositional Logic. The "conventional" notation did not become so until the 1970s and 80s. Some letters in the Polish notation table means a certain word in Polish, as shown:

Concept	Conventional notation	Polish notation	Polish / English word
w:Negation	${\displaystyle \neg \phi }$	Nφ	negation (No)}
Conjunction	${\displaystyle \phi \land \psi }$	Kφψ	conjunction
w:Disjunction	${\displaystyle \phi \lor \psi }$	Aφψ	alternate OR=disjunction
w:Material conditional	${\displaystyle \phi \to \psi }$	Cφψ	implication
w:Biconditional	${\displaystyle \phi \leftrightarrow \psi }$	Eφψ	equivalence'
w:Falsum	${\displaystyle \bot }$	O	False value
w:Sheffer stroke	${\displaystyle \phi \mid \psi }$	Dφψ	Sheffer stroke
Possibility	${\displaystyle \Diamond \phi }$	Mφ	contingent
Necessity	${\displaystyle \Box \phi }$	Lφ	Necessary condition
w:Universal quantifier	Πpφ	kwantyfikator ogólny	ANY: For all p, \phi|Universal quantifier
Existential quantifier	${\displaystyle \exists p\,\phi }$	Σpφ	Exists

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

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See also

• Quantum mechanics
• Quantum biology
• Quantum mechanics
• Photosynthesis
• Mathematical biophysics

• Logique quantique, in Faculté de Physique