Quantum Electrodynamics


Introduction to Quantum Electrodynamics

After R.P. Feynmann, quantum electrodynamics, Oldenbourgh 1992, by quantum electrodynamics one understands the "theory of the interaction between light and matter". Before I turn to the theoretical descriptions, I try to motivate them over an experimental approach, like the one given in T. Mayer - Kuckuck, Atomic Physics, Teubner, study books in physics, 1994.

Mayer - Kuckuck describes the Lamb - SHIFT effect, which can be proven experimentally as "the abolition of the degeneration between the 2 s1/2 and 2 p1/2 level in hydrogen".

The effect is based on a "dilution of the coulomb field" by very small distances (it results in a weaker connection for s - conditions, as for energetically equal p - conditions).

That leads to a fragmentation of the spectral lines in the range of 10-6 eV (electronvolts). The energy difference lies in the microwave range.

How now does this dilution of the coulomb field come off?

One can describe electro-dynamic reciprocal effects by the emission and absorption of quanta. The Coulomb force is caused by the exchange of photons (a photon is a quantum).

A charged particle, e.g. an electron, absorbs and constantly emits quanta:

e - > e + photon - > e

that is possible only under violation of the energy theorem, which is permitted for a very short time, using
the equation  ,  the quantum-mechanical uncertaintyrelation between energy and time. The energy of this photon is negative and its impulse imaginary, one speaks of a "virtual" photon.

The quantum-mechanical wave functions have a complex amplitude and an imaginary exponent, it can be interpreted in the context of multidimensional real mathematics.

"An interaction between two electrons arises, if a virtual photon is exchanged."

One can represent this procedure visually by the so-called Feynman graph.

With very small distances of the charges, deviations from the Coulomb law arise for the working forces, which result from the quantization of the electromagnetic field.

The treatment of the quantum characteristics of the electromagnetic field is the subject of quantum electrodynamics.

The charge density is replaced in the Maxwell Equations  by   and the current through , e.g. by the corresponding terms of the Dirac Equation.

The symbol  indicates the quantum-mechanical wave function, by which a particle is described. The function value of it is a complex number,a real number.
The expression has the dimension 1/m3,  the physical unit of e is [ e ] = C, the physical unit of is C/m3.

The last symbol describes a charge density.

The expression is interpreted often also as spatial probability density of a particle.