Types of quantum field thories
In one of the formulations of the classical mechanics, called Lagrangean formalism, every mechanical system is characterized by its configuration space and a single function called Lagrangian which determines the laws of motion (the initial configuration should be given independently).
The Lagrangian, Lagrangian function or Lagrangean is a real valued function of the points in configuration space and their time derivatives (for some sytems also depending on time), such that the corresponding action principle can be expressed as Euler-Lagrange equations: for all ,
Here is the coordinate in the configuration space.
For continuum systems satisfying reasonable locality, Lagrangians can be expressed in terms of integrating a local quantity, so-called Lagrangian density.
is the corresponding local action functional.
|Lagrangian correspondence||prequantization||prequantized Lagrangian correspondence|