Mathematical signature of photon's and electron's field functions

[birulami]

Is is correct to say that the photon, as an electromagnetic wave, is represented by a function $$\def\R{\mathbb{R}}f:\R^4\to \R^3\times \R^3$$ indicating that each point in 4D spacetime gets assigned a pair of vectors for the electric and the magnetic component respectively?

What are the physical units of the two resulting vectors?

Does the electron also have a field representation? What is its signature? Can I have an example field function? What are the physical units of the resulting values?

Thanks,
Harald.

 

[Xezlec]

I don't think "Classical Physics" is the place to post questions about photons... is it? Photons are quantum.

Is is correct to say that the photon, as an electromagnetic wave, is represented by a function $$\def\R{\mathbb{R}}f:\R^4\to \R^3\times \R^3$$ indicating that each point in 4D spacetime gets assigned a pair of vectors for the electric and the magnetic component respectively?

A photon is represented by a quantum mechanical wave function, I believe. This wave function is complex-valued at every point in 4D spacetime. It's not a 3D vector. The wave function is related to electric and magnetic fields, but I don't claim to know exactly how.

However, it is true that all electromagnetic waves in the classical sense are completely described by the function you've written. Just don't mention photons

What are the physical units of the two resulting vectors?

In classical physics, the units of the electric field (I mean the E-field) are Volts per meter (or Newtons per Coulomb, they mean the same thing). The units of the magnetic field (I mean the B-field) are Teslas.

Note that there are alternate forms of these. Sometimes people talk about the electric field in terms of the D-field, which is the "electric displacement field". This is measured in Coulombs per square meter. And sometimes people talk about the magnetic field in terms of the H-field, which may be called the "auxiliary field". This is in units of Amperes per meter.

Does the electron also have a field representation?

Again, electrons are described by a wave function in quantum physics. That's about all I know. Classically, electrons are just electrons.