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In theoretical physics and applied mathema … In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables. Whereas the "wave equation", the "diffusion equation", and the "continuity equation" all have standard forms (and various special cases or generalizations), there is no single, special equation referred to as "the field equation". The topic broadly splits into equations of classical field theory and quantum field theory. Classical field equations describe many physical properties like temperature of a substance, velocity of a fluid, stresses in an elastic material, electric and magnetic fields from a current, etc. They also describe the fundamental forces of nature, like electromagnetism and gravity. In quantum field theory, particles or systems of "particles" like electrons and photons are associated with fields, allowing for infinite degrees of freedom (unlike finite degrees of freedom in particle mechanics) and variable particle numbers which can be created or annihilated.mbers which can be created or annihilated.
, Równanie pola – równanie, które musi spełn … Równanie pola – równanie, które musi spełniać pole fizyczne, aby opisywało sytuację fizycznie możliwą. Pola spełniające równania polowe nazywa się często polami fizycznymi, a pola ich niespełniające – polami niefizycznymi. Na przykład w mechanice kwantowej obowiązuje równanie Kleina-Gordona, a w teorii względności – równanie Einsteina. Równania pola pozwalają „wymusić” prawa fizyki na ogólnych strukturach matematycznych. Część praw fizyki jest zapisana w samej konstrukcji struktur, ale część musi być postulowana arbitralnie jako równania. Na przykład gdy formułuje się mechanikę Newtona jako działania na wektorach, to w samej konstrukcji wektorów kryje się prawo fizyki stwierdzające, że istnieją trzy wymiary przestrzenne. Z zapisu wektorowego nie wynika natomiast, że wektory reprezentujące przyspieszenie i siłę spełniają drugą zasadę dynamiki – to prawo musi być wyrażone jako równanie pola. Wiele równań pola można wyprowadzić z własności obiektów innych teorii. W ostatnich latach popularne jest rozważanie teorii w większej liczbie wymiarów niż trzy. Różne podstawowe własności pól w wyższych wymiarach okazują się odpowiednikami równań w niższych wymiarach.dpowiednikami równań w niższych wymiarach.
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| rdfs:comment |
In theoretical physics and applied mathema … In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space. Since the field equation is a partial differential equation, there are families of solutions which represent a variety of physical possibilities. Usually, there is not just a single equation, but a set of coupled equations which must be solved simultaneously. Field equations are not ordinary differential equations since a field depends on space and time, which requires at least two variables.me, which requires at least two variables.
, Równanie pola – równanie, które musi spełn … Równanie pola – równanie, które musi spełniać pole fizyczne, aby opisywało sytuację fizycznie możliwą. Pola spełniające równania polowe nazywa się często polami fizycznymi, a pola ich niespełniające – polami niefizycznymi. Na przykład w mechanice kwantowej obowiązuje równanie Kleina-Gordona, a w teorii względności – równanie Einsteina.w teorii względności – równanie Einsteina.
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場の方程式
, Równanie pola
, Field equation
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