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

  1. May 20, 2007 #1
    Is is correct to say that the photon, as an electromagnetic wave, is represented by a function [tex]\def\R{\mathbb{R}}f:\R^4\to \R^3\times \R^3[/tex] 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?

  2. jcsd
  3. May 20, 2007 #2
    I don't think "Classical Physics" is the place to post questions about photons... is it? Photons are quantum.

    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 :smile:

    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.

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