# Principle of least action in field theory

1. Jan 23, 2016

### spaghetti3451

In page 15, Peskin and Schroeder states that

The principle of least action states that when a system evolves from one given configuration to another between times $t_1$ and $t_2$, it does so along the path in configuration space for which $S$ is an extremum.

1. What is the definition of $\textit{configuration}$ - the collection of all generalised spatial coordinates, the scalar field profile as a function of the four coordinates, etc.?
2. What is the definition of $\textit{configuration space}$?

2. Jan 23, 2016

### Orodruin

Staff Emeritus
Configuration space is the space of all possible configurations of a system. If you look at a system with one degree of freedom, it is just the set of possible values for that degree of freedom. If you look at a field, it is the set of all possible field configurations, i.e., the set of all possible ways to assign a field value to each point in space.