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I would like to know which fields in physics have seen growth or benefited by applying QFT? I know that approaches to quantum gravity such as string theory use QFT, HEP and also some branches of condensed matter physics. Where is it applied in condensed matter physics exactly? And in what other areas of theoretical physics, has QFT been applied?

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As DaniH's answer below details, QFT has not merely been applied in some branches of condensed matter. It is the only reasonable language we have for many-body physics, which is a cornerstone of all condensed matter theory. Low-energy nuclear theory (though some might consider that a condensed matter problem...) also requires QFT. – wsc Nov 17 '12 at 17:48
up vote 8 down vote accepted

Quantum field theory, the study of fields from the quantum mechanical point of view, is specially useful to treat interacting many-body systems. It has been applied to low dimensional quantum systems [magnetic like Heisenberg or Ising spin chains or non-magnetic like carbon nanotubes or two-dimensional electron gases], strongly correlated conductors, standard BCS-like superconductors, high-Tc superconductors and a large etc.

Feynman diagrams are commonly used by condensed matter theorists. One example of diagrammatic calculation is done in the $3\text{D}$ electron liquid with long-range Coulomb interactions: we can show that the energy at second order in perturbation theory is not divergent but finite due to renormalization of pure Coulomb interaction by the dynamics of the system. Diagrammatic methods coming from quantum field theory also give a microscopic support to more phenomenological theories, like the Fermi liquid theory. They also allow to perform calculations of conductivity in disordered conductors in the presence of interactions between particles in/or scattering with impurities.

Quantum field theory methods are also used to study $1\text{D}$ fermions [Luttinger liquids]. Luttinger liquid physics appears in many systems like carbon nanotubes, semiconducting quasi-$1\text{D}$ wires, anisotropic crystals or edge states in the fractional quantum Hall effect for example.

Finally, quantum field theory has also been applied to statistical mechanics, for example in the study of quantum phase transitions and critical phenomena where renormalization group methods are commonly applied to obtain critical exponents.

The list can go on and on...

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It is also used to model the early universe in cosmology. In the theory of inflation, the vacuum fluctuations, of a scalar field, are expanded to sizes larger than the Hubble horizon where they then form the seeds of structure formation.

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ohh...yeah, ofcourse...i am looking for some non-trivial answers.. – user7757 Nov 17 '12 at 9:01
I am not sure that early universe cosmology application is that well known. I have added some more details. – Virgo Nov 17 '12 at 16:44

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