Applications of Complex Analysis in Quantum Physics?

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SUMMARY

Complex Analysis plays a crucial role in Quantum Physics, particularly in the application of Green's functions in scattering theory and the use of propagators. Techniques such as Residue calculus are essential for evaluating integrals in quantum field theory, ensuring causality in calculations. Additionally, the 4-epsilon expansion is utilized for dimensions of the Lagrangian/action, which involves analytical continuation. Resources such as the Klein-Gordon equation paper and specific textbooks provide deeper insights into these applications.

PREREQUISITES
  • Complex Analysis, including Residue calculus
  • Quantum Field Theory fundamentals
  • Understanding of Green's functions and propagators
  • Familiarity with Lagrangian mechanics and analytical continuation
NEXT STEPS
  • Study the application of Green's functions in Quantum Physics
  • Learn about the role of Residue calculus in quantum field theory
  • Research the 4-epsilon expansion in Lagrangian formulations
  • Explore analytical continuation techniques in Quantum Mechanics
USEFUL FOR

Students and professionals in physics, particularly those interested in Quantum Physics and its mathematical foundations, as well as mathematicians exploring applications of Complex Analysis in physical theories.

Tacos
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Hi,

I just finished up a Complex Analysis course last term and, though I'm no physics major, I thought Quantum Physics looked interesting.

Does anyone know some common or interesting applications of Complex Analysis within Quantum Physics? Or even an online resource that might delve into one or two of these applications?

Thanks for any assistance!
 
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Green's functions in scattering theory and propagators:

http://en.wikipedia.org/wiki/Propagator

http://www.oberlin.edu/physics/dstyer/StrangeQM/Klein-Gordon.pdf

One does this to ensure causality.

In quantum field theory, a lot of other integrals comes up where you have to know the tricks of Residue calculus to evaluate them.

Also one has 4-epsilon expansion for the dimensions of the Lagrangian/action, and there one uses analytical continuation.

http://books.google.se/books?id=XYt...X&oi=book_result&resnum=1&ct=result#PPA208,M1

page 208 and forward =)
 

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