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,
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
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)
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)
nonrelativistic physics (Nr), governed by the Galiean group of
space-time symmetries, and
relativistic physics (Re), governed by the Poincare group of space-time
the thermodynamic limit (in which the particle number is infinite)
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)
stationary physics (St), in which time is negligible, and
nonequilibrium physics (Ne) where it is not.
the cold limit (where the absolute temperature vanishes)
conservative physics (Co), in which entropy is negligible, and
thermal physics (Th) where it is not.
the flat limit (where the gravitational constant vanishes)
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.
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.
A few examples:
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
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
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
These third level theories describe physics on the usual textbook and
(Maybe someone who likes to do graphics can illustrate this hierarchy
with appropriate diagrams.)
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)
A theoretical physics FAQ