Looking for a textbook introduction to integrals of the following form

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Discussion Overview

The discussion revolves around finding a textbook introduction to integrals related to path integrals in physics, specifically those involving an action defined in terms of a Lagrangian. Participants seek resources that explain the significance of the Lagrangian in the exponent and provide examples of minimizing the action.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant suggests that the integrals in question are related to path integrals and expresses difficulty in searching for relevant materials.
  • Another participant references a Stack Exchange post that discusses the quantity in the exponent of the path integral and mentions Zee’s book "QFT in a Nutshell" as a potential resource, though it is noted to be challenging.
  • A participant confirms they have Zee's book, indicating familiarity with the suggested resource.
  • One participant clarifies that the action is not the entire expression but rather just the integral in the exponent of e, which they find informative.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between the integrals and path integrals, but there is no consensus on the accessibility or clarity of the suggested resources.

Contextual Notes

There are limitations regarding the clarity of the definitions and the specific examples of minimizing the action that participants are seeking.

Who May Find This Useful

Readers interested in theoretical physics, particularly those exploring path integrals and Lagrangian mechanics, may find this discussion relevant.

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):

S = \int dx^4 \Omega \, e^{i \int \mathcal{L} dt}

Where S is an action to be minimized, \Sigma is just something integrable across the 4-volume and \mathcal{L} is a Lagrangian. Ideally, looking for something that:

1. explains why the Lagrangian is in the exponent of e like that and what it signifies, and
2. works an example of minimizing S.

Basically, just want to know where to start.
 
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Sweet. I have Zee.
 
Okay, so first of all it seems the action is *not* the expression, but just the integral in the exponent of e. That's good to know.
 

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