PlanetPhysics/Categorical Physics
Categorical Physics
This is a relatively new area in mathematical and [[../PhysicalMathematics2/|theoretical physics]] that is concerned with category theory applications to physics, especially [[../AbelianCategory3/|non-Abelian categories]] and [[../ModuleAlgebraic/|non-Abelian algebraic topology]] [[../PreciseIdea/|concepts]] and results in [[../QAT/|mathematical physics and physical mathematics]]. Applications range from [[../CategoricalQuantumLMAlgebraicLogic2/|QFT]], [[../NonAbelianQuantumAlgebraicTopology3/|AQFT]], [[../CubicalHigherHomotopyGroupoid/|non-Abelian]] gauge theories and [[../LQG2/|quantum gravity]] to complex [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]], [[../CategoricalDynamics/|categorical dynamics]], [[../CategoricalDynamics2/|complex categorical dynamics]], mathematical biophysics and [[../RSystemsCategory/|relational biology]]. Other applications are related to [[../Bijective/|graph]] theory approaches to Quantum Chemistry.
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References
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- ↑ Baianu, I.C. : \L ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamics). CERN Preprint EXT-2004-059. Health Physics and Radiation Effects (June 29, 2004).
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- ↑ Plymen, R.J. and P. L. Robinson: 1994, Spinors in Hilbert Space , Cambridge Tracts in Math. 114 , Cambridge Univ. Press, Cambridge.
- ↑ Popescu, N.: 1973, Abelian Categories with Applications to Rings and Modules. New York and London: Academic Press., 2nd edn. 1975. (English translation by I.C. Baianu) .
- ↑ Pareigis, B., 1970, Categories and Functors, New York: Academic Press.
- ↑ Pedicchio, M. C. and Tholen, W., 2004, Categorical Foundations, Cambridge: Cambridge University Press.
- ↑ Peirce, B., 1991, Basic Category Theory for Computer Scientists, Cambridge: MIT Press.
- ↑ Pradines, J.: 1966, Th\'eorie de Lie pour les groupoides diff\'erentiable, relation entre propri\'etes locales et globales, C. R. Acad Sci. Paris S\'er. A 268 : 907-910.
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- ↑ M. A. Rieffel : Group C*--algebras as compact quantum metric spaces, Documenta Math. 7 (2002), 605-651.
- ↑ Roberts, J. E.: 2004, More lectures on algebraic quantum field theory, in A. Connes, et al. Noncommutative Geometry , Springer: Berlin and New York.
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- ↑ Szabo, R. J.: 2003, Quantum field theory on non-commutative spaces, Phys. Rep. 378 : 207--209.
- ↑ V\'arilly, J. C.: 1997, An introduction to noncommutative geometry. (at arXiv:physics/9709045)
- ↑ Weinstein, A.: 1996, Groupoids : unifying internal and external symmetry, Notices of the Amer. Math. Soc. 43 : 744--752.
- ↑ Wess J. and J. Bagger: 1983, Supersymmetry and Supergravity , Princeton University Press: Princeton, NJ.