Lecture

Quantum Effective Action

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Description

This lecture introduces the concept of the quantum effective action, explaining how it is related to the correlators in momentum space and how it can be used to organize perturbation theory calculations. The instructor covers the derivation of the effective action from the classical action, the role of connected correlators, and the significance of exact vertices and propagators in the quantum action. The lecture also delves into the properties of the effective action under derivatives, the connection to the Lippmann-Schwinger equation, and the importance of momentum space in understanding the structure of correlators. Additionally, the instructor discusses the calculation of correlators in Euclidean and Minkowski space, highlighting the importance of counter terms in renormalizing the theory.

Official source

Ontological neighbourhood

Physics

Quantum field theory: Topics in quantum field theory

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In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the underlying force laws (codified in a quantum field theory) as the energy scale at which physical processes occur varies, energy/momentum and resolution distance scales being effectively conjugate under the uncertainty principle. A change in scale is called a scale transformation.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) (mɪŋˈkɔːfski,_-ˈkɒf-) combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally.

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Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.

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