Talk:PlanetPhysics/Mathematical Structure of Physical Theories

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This is a contributed topic on the mathematical structures associated with physical theories. Hopefully, this topic will be of interest to both physicists and mathematicians (as well as logicians and philosopy of science researchers).

\section{Mathematical and Logical Foundations of Physics} \subsection{Physical Theories} \begin{itemize} \item Classical, or Newtonian, \htmladdnormallink{mechanics}{http://planetphysics.us/encyclopedia/Mechanics.html}: \htmladdnormallink{Kinematics}{http://planetphysics.us/encyclopedia/NewtonsLawsOfMotion.html} and \htmladdnormallink{Dynamics}{http://planetphysics.us/encyclopedia/NewtonsLawsOfMotion.html}, \htmladdnormallink{Netwon's laws}{http://planetphysics.us/encyclopedia/PrincipleOfCorrespondingStates.html} of \htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} \item Classical \htmladdnormallink{molecular dynamics}{http://planetphysics.us/encyclopedia/CurrentDensityInPlasma.html} \item Classical \htmladdnormallink{Thermodynamics}{http://planetphysics.us/encyclopedia/Thermodynamics.html} and Statistics \item Classical \htmladdnormallink{Electromagnetism}{http://planetphysics.us/encyclopedia/Electromagnetism.html}: Maxwell's theory and \htmladdnormallink{Maxwell's equations}{http://planetphysics.us/encyclopedia/FluorescenceCrossCorrelationSpectroscopy.html} \item Optics and Spectroscopic Theories \item General and \htmladdnormallink{special relativity}{http://planetphysics.us/encyclopedia/SR.html} \item \htmladdnormallink{quantum mechanics}{http://planetphysics.us/encyclopedia/QuantumParadox.html} \item \htmladdnormallink{quantum field theories}{http://planetphysics.us/encyclopedia/SpaceTimeQuantizationInQuantumGravityTheories.html} \item Mathematical Foundations of Quantum Mechanics \item Axiomatic Quantum Field Theories \item Local Quantum Physics theories \item Statistical Quantum Mechanics \item Standard Model (SUSY) \item Electroweak Theory \item Quantum Chromodynamics \item Quantum Gravity theories \item Strings and Branes theories \item Astrophysics theories \item Chaotic Dynamics and Complex \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} theories \item XYZ \end{itemize}

\subsection{Mathematical structures and fields underlying physical theories} \begin{itemize} \item Calculus and Analytical Geometry \item \htmladdnormallink{non-Newtonian calculi}{http://planetphysics.us/encyclopedia/BibliographyForNonNewtonianCalculus.html} \item \htmladdnormallink{vector}{http://planetphysics.us/encyclopedia/Vectors.html} Calculus \item Functional Analysis \item \htmladdnormallink{Differential Geometry}{http://planetphysics.us/encyclopedia/DifferentialGeometry.html} \item Algebra, \htmladdnormallink{matrices}{http://planetphysics.us/encyclopedia/Matrix.html} and \htmladdnormallink{tensors}{http://planetphysics.us/encyclopedia/Tensor.html} \item \htmladdnormallink{category theory}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} \item \htmladdnormallink{algebraic topology}{http://planetphysics.us/encyclopedia/CubicalHigherHomotopyGroupoid.html} and \htmladdnormallink{non-Abelian}{http://planetphysics.us/encyclopedia/AbelianCategory3.html} \htmladdnormallink{algebraic}{http://planetphysics.us/encyclopedia/CoIntersections.html} Theory \item \htmladdnormallink{noncommutative geometry}{http://planetphysics.us/encyclopedia/NoncommutativeGeometry4.html} \item Algebraic Geometry \item Harmonic and Anharmonic Analysis \item Numerical Analysis \item Statistics and Probability Theories \item Model Theory \item Superstructures: supergroups, superalgebras, algebraic supervarieties, \htmladdnormallink{super-categories}{http://planetphysics.us/encyclopedia/SuperCategory6.html} \item XYZ \end{itemize}

\subsection{Logical structure of physical theories}

\begin{itemize} \item Axiomatics and Physical Postulates \item \htmladdnormallink{quantum logics}{http://planetphysics.us/encyclopedia/LQG2.html} \item \htmladdnormallink{automata theory}{http://planetphysics.us/encyclopedia/LQG2.html} and Boolean logic designs \item \htmladdnormallink{quantum automata}{http://planetphysics.us/encyclopedia/QuantumComputers.html} and \htmladdnormallink{quantum computers}{http://planetphysics.us/encyclopedia/LongRangeCoupling.html} \item \htmladdnormallink{many-valued logic}{http://planetphysics.us/encyclopedia/LM_nLogicAlgebra.html} Algebra \end{itemize}

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