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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.
Applications of quantum mechanics include explaining phenomena found in nature as well as developing technologies that rely upon quantum effects, like integrated circuits and lasers. [ note 1 ] Quantum mechanics is also critically important for understanding how individual atoms are joined by covalent bonds to form molecules .
For example, Maxwell's equations of electromagnetism are linear in the electric and magnetic fields, and charge and current distributions (i.e. the sum of two solutions is also a solution); another example is Schrödinger's equation of quantum mechanics, which is linear in the wavefunction.
A field theory tends to be expressed mathematically by using Lagrangians. This is a function that, when subjected to an action principle, gives rise to the field equations and a conservation law for the theory. The action is a Lorentz scalar, from which the field equations and symmetries can be readily derived.
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. [1] [2] [3] In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. [2]
In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by ...
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. [1]: xi QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
These eddies develop a magnetic field which boosts Earth's original magnetic field—a process which is self-sustaining and is called the geomagnetic dynamo. [19] Reversals of Earth's magnetic field. Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior.