Prez Cannady
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Summary:: Pretty sure they have something to do with path integrals, or what not. But obviously it's hard to *search* for this stuff.
Basically, I'm looking for a textbook, any textbook--physics, mathematics, etc.--that deals with integrals that look something like this (mistakes are mine):
[tex]S = \int dx^4 \Omega \, e^{i \int \mathcal{L} dt}[/tex]
Where [itex]S[/itex] is an action to be minimized, [itex]\Sigma[/itex] is just something integrable across the 4-volume and [itex]\mathcal{L}[/itex] is a Lagrangian. Ideally, looking for something that:
1. explains why the Lagrangian is in the exponent of [itex]e[/itex] like that and what it signifies, and
2. works an example of minimizing [itex]S[/itex].
Basically, just want to know where to start.
Basically, I'm looking for a textbook, any textbook--physics, mathematics, etc.--that deals with integrals that look something like this (mistakes are mine):
[tex]S = \int dx^4 \Omega \, e^{i \int \mathcal{L} dt}[/tex]
Where [itex]S[/itex] is an action to be minimized, [itex]\Sigma[/itex] is just something integrable across the 4-volume and [itex]\mathcal{L}[/itex] is a Lagrangian. Ideally, looking for something that:
1. explains why the Lagrangian is in the exponent of [itex]e[/itex] like that and what it signifies, and
2. works an example of minimizing [itex]S[/itex].
Basically, just want to know where to start.