Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Physics
High Energy, Nuclear, Particle Physics
Pauli-Villars regularization for Vacuum Polarization
Reply to thread
Message
[QUOTE="Korybut, post: 6522422, member: 488863"] [B]TL;DR Summary:[/B] In most of the textbooks corresponding integral is computed in ##k^2 <4m^2## assumption. How to extend? Hello! I am currently reading Itzykson Zuber QFT book and on Chapter 7 where for the first time loops are considered. Particular method of dealing with divergences namely Pauli-Villars regularization is considered in section 7-1-1 considering vacuum polarization diagram. I do understand physics here but lost in math. The integral is computed in the textbook but in the assumption ##k^2<4m^2## and the result is the following $$\bar{\omega}(k^2,m,\Lambda)=-\frac{\alpha}{3\pi}\Bigg\{-\log \frac{\Lambda^2}{m^2}+\frac{1}{3}+2\Bigg(1+\frac{2m^2}{k^2}\Bigg[\Bigg(\frac{4m^2}{k^2}-1\Bigg)^{\frac{1}{2}} \times\\ \mathrm{arccot}\Bigg(\frac{4m^2}{k^2}-1\Bigg)^{\frac{1}{2}}-1\Bigg]\Bigg\} $$ I am completely fine with this calculation however the following phrase from the textbook is not clear Please explain why to obtain values for ##k^2>4m^2## one should take this limit. And why discontinuity across the cut does matter here at all. Completely lost... Many thanks in advance. [/QUOTE]
Insert quotes…
Post reply
Forums
Physics
High Energy, Nuclear, Particle Physics
Pauli-Villars regularization for Vacuum Polarization
Back
Top