phase space

Japanese: phase space（英語表記）phasespace

...An important point about the canonical form is that the structure of (2) carries over to relativity, which can be confirmed by writing ( c is the speed of light) in the above example.
[Phase space]
The 2f -dimensional Euclidean space created by the canonical variables q ₁ , …, q _f ; p ₁ , …, p _f is called a phase space, and the solution of (2) is expressed as a set of orbits in this space (different orbits correspond to different initial values), which has the following basic properties: (a) Volume constancy When an arbitrary region of volume V is taken and all the points within it are tracked according to (2), (b) Density constancy Consider a set of dynamical systems that obey (2) and are distributed according to the density function ρ( t , p , q ), the sum of the (state) points entering and leaving the same region as above is always kept to 0. …

*Some terminology explanations that mention "phase space" are listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

Japanese:

…正準形式の重要な点は(2)の構造が相対論にももち越されることで，上例で，とすることで確かめられる(cは光速度)。
［相空間］
　正準変数q₁，……，q_f；p₁，……，p_fの作る2f次元ユークリッド空間を相空間または位相空間phase spaceといい，(2)の解はこの空間における軌道群(異なる軌道は異なる初期値に対応)で表されるが，次のような基本的性質が備わっている。(a)体積不変性　体積Vの任意の領域を取り，その中の点すべてを(2)に従って追跡したとき(b)密度不変性　(2)に従う力学系の集団を考え，密度関数ρ(t,p,q)によって分布しているものとすると，上と同じ領域に出入りする(状態)点の総和はつねに0に保たれる。…