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[parent] Axioms of Physics

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A contributed topic on the Axioms of Physics* in the following areas:

  1. general relativity Theory
  2. Axiomatic and algebraic quantum field theory
  3. quantum algebraic topology
  4. topological quantum field theory (TQFT) and HQFT**
  5. quantum logics and Quantum Computing
  6. Symmetry and Physical Principles and Laws
  7. categorical physics: category theory and groupoid/ topology applications in Physics
  8. Physical Networks and General Dynamics

0.1 Some Fundamental Concepts in Physics

  1. Space, s
  2. Time, t
  3. Spacetime, ST
  4. reference system or Frame of Reference (RS)
  5. Motion
  6. Measurement
  7. observable
  8. Universal constants: Planck’s constant (h, the speed of light, c, gravitational constant, G; hyperfine constant, e; cosmological constant, λ
  9. Matter
  10. mass
  11. particle
  12. Elementary Particles and quarks
  13. energy: Conservation Laws, Hamiltonian operator, energy eigenvalues. eigenstates, Lagrangian, Photons/Electromagnetic radiation
  14. Fields: Electromagnetic, magnetic, electrical; nuclear; gravitational
  15. Gravity
  16. String/strings

References

[1]   Isaac Newton. 1686.Principles of Natural Philosophy.

[2]   “Works of Sir Isaac Newton–Isaaci Newtoni Opera quae exstant omnia”

[3]   Albert Einstein. 1956. Relativity Theory. NL

[4]   Dirac, Paul A.M. 1958. Principles of Quantum Mechanics. NL

[5]   Richard Feynman. 1965. Lecture Notes in Physics. NL

[6]   Stephen Weinberg. 1994. Quantum FieldTheory. NL

[7]   Eilenberg, S., and Kelly, G.M., Closed Categories, Proceedings of the Conference on Categorical Algebra (La Jolla 1965), Springer Verlag 1966.

[8]   Eilenberg, S., and Mac Lane, S., General Theory of Natural Equivalences, Trans. Amer. Math. Soc. 58, 231–294 (1945).

[9]   Kan, D. M., Adjoint Functors, Trans. Amer. Math. Soc. 87, 294–329 (1958).

[10]   Lawvere, F. W., Functorial Semantics of Algebraic Theories, Proc. Nat. Acad. Sc. U.S.A.,50, 869–872 (1963).

[11]   Lawvere, F. W., The Category of Categories as a Foundation for Mathematics, Proceedings of the Conference on Categorical Algebra (La Jolla 1965), Springer Verlag. 1966.

(See also the Review 7332 by J. Isbell, Dec. 1967, Math. Reviews).

[12]   Mac Lane, S., Categorical Algebra, Bull. Amer. Math. Soc., 71, 40–106 (1965).

0.2 Remarks

*1. Unlike Mathematical Axioms that have all terms defined mathematically, the Axioms of Physics, oftentimes called “Postulates”, are defined in terms of physical concepts that may also relate to measurements and may include basic physical assumptions derived on an experimental and physical-conceptual basis, such as the fundamental axiom of Local Quantum Field Theory, or Axiomatic Quantum Field Theory, also called Algebraic Quantum Field Theory (AQFT), that all quantum measurement and observations involve local interactions in spacetime.

**2. Homotopy and Quantum Field Theory


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See Also: Fundamental physical concepts, physical laws

Keywords:  axioms, foundations of physics, theoretical physics, QFT, AQFT, TQFT, General Relativity theory

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Cross-references: radiation, Lagrangian, Hamiltonian operator, energy, quarks, particle, mass, light, speed, observable, reference system, groupoid, category theory, categorical physics, quantum logics, TQFT, quantum field theory, topological, quantum algebraic topology, algebraic quantum field theory, general relativity
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This is version 16 of Axioms of Physics, born on 2010-06-05, modified 2026-10-07.
Object id is 871, canonical name is AxiomsOfPhysics.
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Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )

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