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Application of quantum field theory to condensed matter physics

  1. Apr 19, 2008 #1
    i've read that quantum field theory can be applied to condensed matter physics but i don't understand how: quantum field theory is the union of SR with QM but how is SR related to condensed matter physics? i understand that quantum field theory would be useful because it can describe many-particle systems but i've read about it being applied to the thermodynamics of solids at temperatures near absolute zero - how could SR possibly be related to this?
    someone please help me understand :smile:
  2. jcsd
  3. Apr 19, 2008 #2
    Through my shallow understanding, they are linked through Entropy-Information Theory.
    I might be wrong though.
  4. Apr 19, 2008 #3


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    Most of modern condensed matter physics is field theory, and of course the former has greatly advanced understanding of the latter (for instance the Higgs mechanism was independantly found by condensed matter theorists). They simply take the nonrelativistic limit in most cases.

    Its useful b/c ultimately its a formalism to deal with the many body problem.
  5. Apr 19, 2008 #4


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    As Haelfix has stated, it is most widely used in the treatment of many-body physics. The best introduction to it is Mattuck's book "A Guide to Feynman Diagrams in the Many-Body Problem".

    All QFT need not be relativistic, or at least, not dealing with relativistic effects, in condensed matter physics.

  6. Apr 20, 2008 #5
    what does the SR mean?
  7. Apr 20, 2008 #6
    Special relativity.
  8. Apr 20, 2008 #7
    As people have pointed out, QFT doesn't really have anything to do with special relativity. It is fundamentally the study of fields, from a quantum point of view. These field *can* be relativistic, and currently QFT really the only mainstream accepted way to do quantum mechanics in a relativistic manner. However, nothing constrains it to that arena.

    Most frequently in condensed matter, we approximate some macroscopic system as a set of interacting fields. For instance, lattices can be approximated as an elastic continuum for the purposes of looking at phonons. However, due to the real intrinsic lower bound on the scale of the system, the theory has a frequency cut-off --- something which is very general in condensed matter field theory.
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