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What is a field?

  1. Sep 10, 2010 #1
    What is a field in quantum mechanics (not the classical version)? And when it is said that an electron is an "excitation state of a field", does that mean that electrons are created by wave or disturbances in a field? Also, is there a different type of field for each fundemental particle, or can it be simplified to one big field?
     
  2. jcsd
  3. Sep 11, 2010 #2

    tom.stoer

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    You have to study quantum field theory.

    What one does is (roughly speaking) the following. One takes the Dirac field (mathematically it is a classical field), takes it's Fourier transform and translates the Fourier components b(p), b*(p) and d(p) d*(p) into operators. This step is called quantization. For each three-momentum p there are these operators which are related to the creation and annihilation operators in case of the harmonic oscillator. That means a plane wave with a certain momentum p is "created" in the Hilbert space using a creation operator. Attention: there is not only one pair, but two pairs for each p.

    One needs a field for each particle, e.g. one field for the photon (4-potential), one for the electron and the positron, one for the quarks (the different colors are treated via indices, so the field becomes a 4-spinor with an additional color-index i=1..3), one for the gluon (4-potential now with a color index a=1..8) etc.

    Finding one big field is the dream of theoretical physicists in the context of a "theory of everything". String theory (a much debated, partial controversial issue) comes rather close to this dream, as there is only one string.
     
  4. Sep 11, 2010 #3
    OK, thanks for clearing everything up :)
     
  5. Sep 12, 2010 #4

    tom.stoer

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    really, everything?
     
  6. Sep 12, 2010 #5
    Do you have any papers or references to someone performing those operations? Id be interested to see...
     
  7. Sep 12, 2010 #6

    tom.stoer

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    Every book on quantum field theory will do.

    I recommend
    - Ryder
    - Weinberg
    - Srednicki (draft: http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf; [Broken]; chaper 3 Canonical Quantization of Scalar Fields)
     
    Last edited by a moderator: May 4, 2017
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