The Physics and Astronomy Classification Scheme (PACS), ''an internationally adopted, hierarchical subject classification scheme, designed by the American Institute of Physics (AIP)'', partitions physics into

  • the physics of elementary particles and fields,
  • nuclear physics,
  • atomic and molecular physics,
  • electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics,
  • physics of gases, plasmas, and electric discharges,
  • condensed matter: structural, mechanical and thermal properties,
  • condensed matter: electronic structure, electrical, magnetical, and optical properties,
  • interdisciplinary physics and related areas of science and technology,
  • geophysics, astronomy, and astrophysics.

    As a complement to this classification, I propose a systematic view of physics not by its phenomena but by classifying it in terms of the following seven orthogonal criteria.

  • The first criterion is methodological, and distinguishes between applied physics (AP), didactical physics (DP), experimental physics (EP), theoretical physics (TP), and mathematical physics (MP).
    The other six criteria are defined in terms of the six limits that play an important role in physics:
  • the classical limit (in which Planck's constant vanishes) distinguishes between classical physics (Cl), in which all quantities commute, and quantum physics (Qu) where noncommutative quantities exist.
  • the nonrelativistic limit (in which the speed of light is infinite) distinguishes between nonrelativistic physics (Nr), governed by the Galiean group of space-time symmetries, and relativistic physics (Re), governed by the Poincare group of space-time symmetries.
  • the thermodynamic limit (in which the particle number is infinite) distinguishes between macroscopic physics (Ma), in which microscopic details are negligible, and microscopic physics (Mi) where they are not.
  • the eternal limit (of infinite amount of time passed) distinguishes between stationary physics (St), in which time is negligible, and nonequilibrium physics (Ne) where it is not.
  • the cold limit (where the absolute temperature vanishes) distinguishes between conservative physics (Co), in which entropy is negligible, and thermal physics (Th) where it is not.
  • the flat limit (where the gravitational constant vanishes) distinguishes between physics in flat space-time (Fl), in which curvature is negligible, and general relativistic physics (Gr) where it is not.
    A particular subfield is characterized by a signature consisting of choices of labels (or double arrows between labels) in some categories.

    A few examples:

  • Thermodynamics: Ma ,Th
  • Equilibrium thermodynamics: Ma, Th, St
  • Classical Mechanics: Cl, Co
  • Classical field theory: Cl, Co, Ma
  • General relativity: Cl, Re, Ma, Gr
  • Quantum mechanics: Qu, Nr
  • Relativistic quantum field theory: TP, Qu, Re, Mi
  • Statistical mechanics: TP, Mi<-->Ma, Th
  • Precision tests of the standard model: TP<-->EP, Qu, Re, Mi, St, Co
  • The empty signature is simply the field of physics itself.

    In each category, one can choose no label, a single label, or an arrow between two labels, giving 1+5+5*4/2=16 cases for the first category, and 1+2+1=4 cases in the six other categories. Thus the classification splits physics hierarchically into 16*4^6=65536 potential subfields with different signatures, of which of course only the most important ones carry conventional names.

    Let me give what I think is a particularly useful subhierarchy of the complete hierarchy. This subhierarchy splits the whole physics recursively into quadrangles of subfields.

    On the highest first level, we split physics according to the cold limit and the flat limit. This gives a quadrangle of first level theories of

  • thermal physics in curved space-time (Th Cu)
  • thermal physics in flat space-time (Th Fl)
  • conservative physics in curved space-time (Co Cu)
  • conservative physics in flat space-time (Co Fl) together with two first level interface theories
  • statistical physics (Th<-->Co)
  • geometrization of physics (Cu<-->Fl)

    These first level theories describe very general principles on the theoretically most fundamental level of physics.

    On the second level, we split each first level theory according to the eternal limit and the thermodynamic limit. This gives in each case a quadrangle of theories of

  • nonequilibrium particle physics (Ne Mi)
  • nonequilibrium thermodynamics (Ne Ma)
  • physics of bound states and scattering (St Mi)
  • equilibrium thermodynamics (St Ma) together with two second level interface theories
  • long time asymptotics (Ne<-->St)
  • thermodynamic limits (Ma<-->Mi)

    These second level theories describe physics on a level already close to many applications, especially outside physics, though still lacking detail.

    On the third, lowest level, we split each second level theory according to the nonrelativistic limit and the classical limit. This gives in each case a quadrangle of theories of

  • relativistic quantum physics (Re Qu)
  • relativistic classical physics (Re Cl)
  • nonrelativistic quantum physics (Nr Qu)
  • nonrelativistic classical physics (Nr Cl) together with two third level interface theories
  • nonrelativistic limit (Re<-->Nr)
  • quantization and classical limit; quantum-classical systems (Qu<-->Cl)
    These third level theories describe physics on the usual textbook and research level.

    (Maybe someone who likes to do graphics can illustrate this hierarchy with appropriate diagrams.)

    Arnold Neumaier (
    A theoretical physics FAQ