This is a new, contributed topic entry on subfields and topics of mathematical physics and applied mathematics.

Topics in applied mathematical physics and physical mathematics

1. Non-equilibrium Thermodynamics and statistical mechanics
2. computational physics
3. molecular dynamics experiments (MDE) or computer simulations
4. plasma wave non-linear excitation
5. Maxwell's equations for Relativistic electron pulses
6. Theoretical geophysics and physico-mathematical models in geophysics
7. Astrophysics, cosmology, geometrodynamics and general relativity theories
8. quantum gravity
9. quantum logics, including LM-logic algebras
10. quantum state spaces, quantum operators, superoperators, observables, eigenstates
11. Hamiltonians and other Hermitian operators
12. Algebraic quantum field theory (AQFT)
13. Quantum Algebraic Topology (QAT)
14. quantum operator algebra (QOA) in quantum field theories and quantum gravity
15. quantum groups, Hopf algebras, quantum supergroups and superalgebras
16. topological quantum field theories (TQFT)
17. homotopy quantum field theories (HQFT)
18. non-Abelian physics
19. non-Newtonian physics or non-Newtonian behavior; examples are non-Newtonian flows in rheology, such as plastic flows, pseudo-plastic flows and dilatant flows; Special Relativity and Quantum theories can also be considered as examples of non-Newtonian fields of Physics, whereas molecular dynamics experiments or simulations that are based on Netwon's laws of motion, or Newton's Principia, are obviously Newtonian computations; Leibnitz's infinitesimal calculus approach to analysis can be thus also considered as a non-Newtonian analytical calculus.
20. non-Newtonian calculus
21. unified field theories in physics, supersymmetry and spontaneous symmetry breaking
22. CPT symmetry and parity violation
23. Quantum chromodynamics (QCD): quarks, parton distributions, nuclear spin structures and theories of Nuclear Fusion (NF)
24. Elementary particle theories and Higgs bosons
25. quantum geometry and non-commutative geometry applications to SUSY model in physics
26. Harmonic and anharmonic analysis of quantum systems
27. Bibliography for mathematical physics and quantum algebraic topology
28. Geometry and group theory applications to mathematical crystallography
29. spinors and spin groups: spin networks, spin foams, vectors, matrices, tensors and twistors
30. Complex systems structure (CSS) and dynamics (CSD)
31. solitons and semi-classical systems
32. Systems with Chaos
33. Topological dynamics
34. Biotopology and topology applications in biology, non-random Networks: cellular, neural and genetic
35. fluid dynamics, including aerodynamic and vorticity field models with applications in Aeronautics, rocketry and space exploration (NASA, etc.)
36. superfluids and superconductivity: low- and high- temperature mechanisms
37. Non-crystalline systems, paracrystals and glasses
38. categorical physics and categories/ in biology
39. Categorical dynamics and biodynamics
40. Physical vs. mathematical probability
41. Applied statistical mechanics
42. Numerical analysis and measurement theory in physics
43. Biostatistics
44. Bibliography for statistical mechanics
45. Bibliography for mathematical physics and quantum algebraic topology
46. Computational physics and astrophysics
47. computer models and automata theory in biology and medicine
48. Mathematical medicine and epidemiological models
49. quantum automata and quantum computers
50. quantum nanoautomata and nanorobots
51. Mathematics in natural/life sciences
52. mathematical biology and theoretical biophysics
53. Mathematical biophysics
54. bibliography for mathematical biophysics
55. Mathematics of finance and market predictions
56. Mathematical and mathematical physics applications to population genetics
57. Quantum genetics and bioinformatics
58. Mathematics and mathematical physics applications in electrical engineering and bioengineering
59. mathematical physics and physical mathematics models applications in geophysics and ecology
60. Mathematical physics and physical mathematics models in energy science and engineering, alternative energy mathematical models and theories