Quantum field theory

Quantum field theory (QFT) is the application of quantum mechanics to fields. It provides a theoretical framework, widely used in particle physics and condensed matter physics, in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed. Non-relativistic quantum field theories are needed in condensed matter physics— for example in the BCS theory of superconductivity. Relativistic quantum field theories are indispensable in particle physics (see the standard model), although they are known to arise as effective field theories in condensed matter physics.

Renormalization

The essence of quantum field theory is renormalization. A single particle state in quantum field theory incorporates within it multiparticle states. This is most simply demonstrated by examining the evolution of a single particle state in the interaction picture—

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::|psi(t) angle = e^{iH_It} |psi(0) angle = left |psi(0) angle.

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Taking the overlap with the initial state, one retains the even powers of HI. These terms are responsible for changing the number of particles during propagation, and are therefore quintessentially a product of quantum field theory. Corrections such as these are incorporated into wave-function renormalization and mass renormalization. Similar corrections to the interaction Hamiltonian, HI, include vertex renormalization, or, in modern language, effective field theory.

Related Topics:
Wave-function renormalization - Mass renormalization - Hamiltonian - Vertex renormalization - Effective field theory

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