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If the matter field is taken so as to describe the interaction of electromagnetic fields with the Dirac electron given by the four-component Dirac spinor field ψ, the current and charge densities have form: [2] = † = †, where α are the first three Dirac matrices. Using this, we can re-write Maxwell's equations as:
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In QFT, the former is called the free field part of the model, and the latter is called the interaction part. The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using the Dyson series.
For example, an electromagnetic field has both electric field strength and magnetic field strength. As an application, in radio frequency telecommunications, the signal strength excites a receiving antenna and thereby induces a voltage at a specific frequency and polarization in order to provide an input signal to a radio receiver.
The matrix form of the field tensor yields the following properties: [3] Antisymmetry: = Six independent components: In Cartesian coordinates, these are simply the three spatial components of the electric field (E x, E y, E z) and magnetic field (B x, B y, B z).
The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: = [′ ′ + ′ (′ ′) + ′] = ′ Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light.
The EFIE describes a radiated field E given a set of sources J, and as such it is the fundamental equation used in antenna analysis and design. It is a very general relationship that can be used to compute the radiated field of any sort of antenna once the current distribution on it is known.
Poynting vector in a static field, where E is the electric field, H the magnetic field, and S the Poynting vector. The consideration of the Poynting vector in static fields shows the relativistic nature of the Maxwell equations and allows a better understanding of the magnetic component of the Lorentz force , q ( v × B ) .