|
In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called ''path'' or ''history'', of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths.〔McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B. Parker, 1994, ISBN 0-07-051400-3〕 Action has the dimensions of ()·(), and its SI unit is joule-second. This is the same unit as that of angular momentum. ==Introduction== Empirical laws are frequently expressed as differential equations, which describe how physical quantities such as position and momentum change continuously with time. Given the initial and boundary conditions for the situation, the "solution" to these empirical equations is an implicit function describing the behavior of the system. There is an alternative approach to finding equations of motion. Classical mechanics postulates that the path actually followed by a physical system is that for which the action is minimized, or, more generally, is stationary. In other words, the action satisfies a variational principle: the principle of stationary action (see also below). The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. This simple principle provides deep insights into physics, and is an important concept in modern theoretical physics. The equivalence of these two approaches is contained in Hamilton's principle, which states that the differential equations of motion for ''any'' physical system can be re-formulated as an equivalent integral equation. It applies not only to the classical mechanics of a single particle, but also to classical fields such as the electromagnetic and gravitational fields. Hamilton's principle has also been extended to quantum mechanics and quantum field theory—in particular path integral formulation makes use of the concept—where a physical system follows simultaneously all possible paths with probability amplitudes for each path being determined by the action for the path.〔Quantum Mechanics, E. Abers, Pearson Ed., Addison Wesley, Prentice Hall Inc, 2004, ISBN 978-0-13-146100-0〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Action (physics)」の詳細全文を読む スポンサード リンク
|