Looking for a textbook introduction to integrals of the following form

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SUMMARY

The discussion focuses on finding a textbook introduction to integrals related to path integrals, specifically in the context of physics and mathematics. The integral in question is represented as S = ∫ dx^4 Ω e^{i ∫ ℒ dt}, where S denotes the action to be minimized, ℒ is the Lagrangian, and Ω is an integrable function across the 4-volume. Participants recommend Zee’s book "QFT in a Nutshell" for its relevance, despite its complexity, and emphasize the importance of understanding the role of the Lagrangian in the exponent of the exponential function.

PREREQUISITES
  • Understanding of path integrals in quantum field theory
  • Familiarity with Lagrangian mechanics
  • Basic knowledge of integrals in multiple dimensions
  • Experience with mathematical notation used in physics
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  • Research the concept of path integrals in quantum mechanics
  • Study Lagrangian mechanics and its applications in physics
  • Explore examples of minimizing action in variational calculus
  • Read "QFT in a Nutshell" by Anthony Zee for advanced insights
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Students and professionals in physics, particularly those interested in quantum field theory, as well as mathematicians looking to understand the application of integrals in physical contexts.

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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