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B Why is there a quantum field?

  1. Feb 24, 2017 #1
    Are there thoughts as to why there is a quantum field. Does it arise from something more fundamental?
    Thanks for considering.
     
  2. jcsd
  3. Feb 24, 2017 #2

    Drakkith

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    Staff: Mentor

    As far as I understand it, fields in Quantum Field Theory are fundamental. Especially since fundamental particles themselves are merely excitations of the underlying field.
     
  4. Feb 24, 2017 #3
  5. Feb 24, 2017 #4

    Drakkith

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    Staff: Mentor

  6. Feb 24, 2017 #5
    Quantum fields are necessary because it isn't possible to formulate a self-consistent relativistic quantum theory of a single particle, or of a fixed number of particles (this isn't surprising since relativity allows for the conversion of energy to mass and vice versa). A relativistic quantum theory of particles must necessarily allow for varying numbers of particles and particle types, and this can only be fruitfully implemented with the use of fields (this also true in non-relativistic quantum mechanics, where a system containing a varying number of particles is usually analyzed using quantum fields).
     
  7. Feb 24, 2017 #6

    bhobba

    Staff: Mentor

    Dirac gave EM a quantum injection to create the first quantum field theory. In this way photons emerged naturally. Could it be all particles emerge the same way? So field theories of Electrons were cooked up and sure enough electrons could be explained similarly. Then it was realised - well electrons carry an electric field - it would be rather difficult to have a combined theory unless they were both field theories - so Quantum Electrodynamics (QED) was borne.

    Then one Dr Julian Schwinger came along and showed that if one writes down a general theory of fields - one for spin 1/2 particles (which electrons are) and one for spin one particles (which photons are) you notice something interesting - they have global U(1) symmetry without detailing exactly what it is (it simple - but its better if you look it up), But relativity says it should really be local - not global. So we check local U(1) symmetry - drats - it fails - an extra term appears when you try it. But it jumps out at you - its very easy to cancel that term if you add a term to the combined filed theory - you do this and - lo and behold - we have the equation of QED.

    Now it turns out if you try the same trick but demand SU(2) symmetry - you get the W, Higgs etc ie the electroweak theory. Then we do it for SU(3) symmetry and lo and behold you get quarks.

    All this has convinced physicists that everything is fundamentally a quantum field that obeys certain local symmetry rules - in fact its the 3 simplest symmetries U(1), SU(2), and SU(3). Why? Well its very beautiful but exactly why is a deep, deep, mystery. Nobel's galore to those that can sort it out. String theory may - but so far has fallen short. Last I heard it gets so tantalizingly close you want to cry - but sorry - no cigar - yet.

    You can find the technical detail for these claims here:
    https://www.amazon.com/Physics-Symmetry-Undergraduate-Lecture-Notes/dp/3319192000

    In fact it turns the process on it's head and finds those equations via symmetry then shows how QFT and particles reasonably emerge. Even standard QM emerges in the same way - its a quite different approach.

    For example you look at the most general symmetries a complex field can have. If it has spatial symmetry then a certain operator (the QM momentum operator P) is conserved. But what does it mean to apply such an operator to a field? Well reasonably if u is the field and you have Pu = pu where p is a number you can say that the field has momentum p. That way you get the eigenvalue interpretation. But what if u is not an eigenvector? That's where one must evoke the Born Rule - why the Born rule - well it just seems that's how nature is - with due deference to Gleason which can justify it somewhat (the main ingredient is non contextuality and a willingness to introduce probabilities).

    Thanks
    Bill
     
    Last edited by a moderator: May 8, 2017
  8. Feb 25, 2017 #7
     
    Last edited by a moderator: May 8, 2017
  9. Feb 25, 2017 #8
    Excellent! Thanks for all the thoughts on this. I appreciated the broad-picture historical walk through, Bill.
    It seems odd to have this inherently restless and resonant drum head (the field) without the drum.
     
  10. Feb 25, 2017 #9
    Here are links to two internet articles written by the Physicist, Brian Skinner. In the second article he tells us where the electron field comes from. In the first article he gives a very nice definition of a field.

    https://www.ribbonfarm.com/2015/06/23/where-do-electric-forces-come-from/

    https://www.ribbonfarm.com/2015/08/20/qft/

    Here is a quote from the first article

    And here is a quote from the second article

     
  11. Feb 25, 2017 #10
  12. Feb 25, 2017 #11
    Thanks, good perspective. Comforting to find with a physicist a place where we both know nothing. Best.
     
  13. Feb 25, 2017 #12
    If you get a chance, please do read the second article above. It really gets good (and is simple). Here, again, is a link to it.

    https://www.ribbonfarm.com/2015/08/20/qft/

    And here is a quote to get you interested...

     
  14. Feb 26, 2017 #13
    When state vector reduced to a random value (or what they call collapse of the wave function or born rule activated).. what happens in the field version.. is the field behavior smooth or undergoes sudden break.. like sea wave or tsunami moving in one place then suddenly appearing elsewhere (random behavior from the deterministic schoedinger equeation prior to reduction)?
     
    Last edited by a moderator: May 8, 2017
  15. Feb 26, 2017 #14

    bhobba

    Staff: Mentor

    At your level that's not a bad description. It suddenly collapses to like a knot in the field.

    You should get the following:
    https://www.amazon.com/Fields-Color-theory-escaped-Einstein/dp/0473179768

    The kindle version is dirt cheap.

    Thanks
    Bill
     
    Last edited by a moderator: May 8, 2017
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