Application of quantum field theory to condensed matter physics

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Discussion Overview

The discussion revolves around the application of quantum field theory (QFT) to condensed matter physics, exploring the relationship between special relativity (SR) and condensed matter systems, particularly in the context of many-particle systems and thermodynamics at low temperatures.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how SR relates to condensed matter physics, questioning the relevance of QFT in this context.
  • Another participant suggests a connection through Entropy-Information Theory, although they express uncertainty about this claim.
  • A different participant asserts that modern condensed matter physics heavily relies on field theory, noting that the nonrelativistic limit is often taken in practice.
  • It is mentioned that QFT is useful for addressing the many-body problem, with a reference to a specific book for further reading.
  • Clarification is provided that QFT does not necessarily involve relativistic effects in condensed matter physics.
  • Participants seek clarification on the meaning of "SR," which is confirmed to refer to special relativity.
  • One participant reiterates the initial confusion about the relationship between QFT and SR, emphasizing that QFT fundamentally studies fields from a quantum perspective, which can be non-relativistic in condensed matter applications.
  • It is noted that macroscopic systems in condensed matter can be approximated as interacting fields, with examples like lattices being treated as elastic continua for phonon analysis.
  • A point is raised regarding the existence of a frequency cut-off in condensed matter field theory due to intrinsic limitations on the scale of the system.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement regarding the application of QFT to condensed matter physics. There is no consensus on the relationship between SR and condensed matter, and multiple viewpoints are presented without resolution.

Contextual Notes

The discussion highlights limitations in understanding the connections between QFT and condensed matter physics, particularly regarding the role of SR and the implications of non-relativistic approximations.

chris_183
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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:
 
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Through my shallow understanding, they are linked through Entropy-Information Theory.
I might be wrong though.
 
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.
 
chris_183 said:
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:

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.

Zz.
 
what does the SR mean?
 
aegeansea said:
what does the SR mean?

Special relativity.
 
chris_183 said:
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:

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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