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Principle of least action in field theory

  1. Jan 23, 2016 #1
    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. jcsd
  3. Jan 23, 2016 #2


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    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.
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