Quantum Field Theory

The quantum field theory is the study of fields from a quantum mechanical perspective and is especially useful in treating interacting many-body systems. The theory has been applied to low dimensional quantum systems like the 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 frequently used by condensed matter theorists. One example of diagrammatic calculation is done in the 3D electron liquid with long-range Coulomb interactions. It has been shown 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. Schematic representation methods derived from quantum field theory also give a miniscule support to more phenomenological theories, like the Fermi liquid theory. Calculations of conductivity can be performed in disordered conductors in the presence of interactions between particles in/or scattering with impurities. The quantum field theory methods are also used to study 1-D fermions. Luttinger liquid physics appears in many systems like carbon nanotubes, semiconducting quasi-1D wires, anisotropic crystals or edge states in the fractional Quantum Hall effect for example. The further applications of the quantum field theory have been applied to statistical mechanics, in the study of quantum phase transitions and critical phenomena.

  • Nonrelativistic quantum theory
  • Feynman diagram
  • De Broglie wavelength
  • Wentzel-Kramers-Brillouin method
  • Compton effect
  • Quantized electronic structure (QUEST)
  • Positronium
  • Fermi liquid theory

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