Why do we use Monte Carlo in order to calculate the VEV?

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SUMMARY

The discussion centers on the necessity of using Monte Carlo methods, specifically Markov Chain Monte Carlo (MCMC), to calculate vacuum expectation values (VEV) in quantum field theory (QFT). The participant, an undergraduate student, questions the motivation for employing MCMC when exact solutions, such as those derived from path integrals, are available for simple systems like the simple harmonic oscillator (SHO). The conclusion drawn is that MCMC is essential for evaluating VEVs in complex systems where exact integrals cannot be computed, particularly when dealing with non-trivial actions.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with Monte Carlo methods, specifically Markov Chain Monte Carlo (MCMC)
  • Knowledge of path integrals and their applications in physics
  • Basic concepts of vacuum expectation values (VEV)
NEXT STEPS
  • Study the applications of MCMC in complex quantum systems
  • Learn about path integrals and their limitations in QFT
  • Explore advanced topics in Quantum Field Theory, focusing on non-trivial actions
  • Investigate alternative numerical methods for evaluating VEVs
USEFUL FOR

Students and researchers in theoretical physics, particularly those interested in quantum field theory and computational methods for evaluating vacuum expectation values.

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Homework Statement


It's not homework.
It's just a simple question occurred when I'm reading Monte Carlo method in QFT by Colin Morningstar.
Of course, I didn't study the QFT earlier. I'm just a regular(or retarded) undergraduate student and I just wanted to learn MCMC technique, and hoped to learn some applications of MCMC in physics.
I thought I got the basic idea and already programmed the first example of SHO.
However, I noticed he didn't provide proper motivation for MCMC method in order to evaluate vacuum expectation.
He provided exact solution of SHO deduced from the path-integral by hand.

So, I am wondering now. Why do we have to use MCMC to calculate the VEV, if we are able to calculate exact integral?


Homework Equations





The Attempt at a Solution



I thought about path integral from what kind of action cannot be calculated.
It rules out actions from constant potential, harmonic potential, and Coulomb potential.

It's my first posting in this site. If I am violating some kind of rules of this site, please let me know.
 
Physics news on Phys.org
Never mind. It was stupid question.
I think I got the answer.
 

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