Imaginary Time and Path Integrals?

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SUMMARY

In the discussion regarding Steven Hawking's assertion in "A Brief History of Time," it is established that time may possess an imaginary component to facilitate Feynman's Sum-Over-Histories approach. The key concept involved is the convergence of the integral, which is achieved through a mathematical technique known as Wick rotation. This method transforms real time into imaginary time, allowing for the necessary convergence in quantum field theory calculations.

PREREQUISITES
  • Understanding of Feynman's Sum-Over-Histories approach
  • Familiarity with quantum field theory
  • Knowledge of mathematical techniques, specifically Wick rotation
  • Basic grasp of integrals and their convergence properties
NEXT STEPS
  • Research the mathematical implications of Wick rotation in quantum mechanics
  • Study Feynman's path integral formulation in detail
  • Explore the concept of imaginary time in theoretical physics
  • Investigate the convergence of integrals in quantum field theory
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The discussion is beneficial for physicists, particularly theoretical physicists and quantum mechanics researchers, as well as students seeking to deepen their understanding of advanced concepts in quantum field theory.

LarryS
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Steven Hawking writes in A Brief History of Time that time itself must sometimes have an imaginary component in order for Feynman's Sum-Over-Histories approach to work. Why, in a nutshell, is this so? Thanks in advance.
 
Physics news on Phys.org
Convergence of the integral.
 
It is wick rotation, please google "wick rotation",
you also can find wick rotation in Wiki
 

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