Looking for a textbook introduction to integrals of the following form

AI Thread Summary
The discussion centers on seeking a textbook that covers integrals related to path integrals in physics, particularly those involving actions and Lagrangians. The integral in question is expressed as S = ∫ dx^4 Ω e^(i ∫ ℒ dt), where S represents an action to be minimized, Ω is an integrable function across a four-dimensional volume, and ℒ is the Lagrangian. Key points of interest include understanding the significance of the Lagrangian being in the exponent and examples of minimizing S. A reference to Zee's "QFT in a Nutshell" is made, though it is noted that the book is challenging. The discussion clarifies that the action is not the entire expression but specifically the integral in the exponent.
Prez Cannady
Messages
21
Reaction score
2
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.
 
Physics news on Phys.org
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.
 
The book is fascinating. If your education includes a typical math degree curriculum, with Lebesgue integration, functional analysis, etc, it teaches QFT with only a passing acquaintance of ordinary QM you would get at HS. However, I would read Lenny Susskind's book on QM first. Purchased a copy straight away, but it will not arrive until the end of December; however, Scribd has a PDF I am now studying. The first part introduces distribution theory (and other related concepts), which...
I've gone through the Standard turbulence textbooks such as Pope's Turbulent Flows and Wilcox' Turbulent modelling for CFD which mostly Covers RANS and the closure models. I want to jump more into DNS but most of the work i've been able to come across is too "practical" and not much explanation of the theory behind it. I wonder if there is a book that takes a theoretical approach to Turbulence starting from the full Navier Stokes Equations and developing from there, instead of jumping from...
Back
Top