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

  • Thread starter HighOnAcid
  • Start date
  • Tags
    Monte carlo
In summary, the speaker is a undergraduate student who is trying to learn about Monte Carlo method in QFT by Colin Morningstar. They have already programmed an example of SHO, but are now wondering why MCMC is necessary for calculating the vacuum expectation value (VEV) if the exact integral can be calculated. They also mention considering which actions cannot be calculated, such as those from constant, harmonic, and Coulomb potentials. They apologize for any rule violations and state that they have found the answer.
  • #1
HighOnAcid
2
0

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
  • #2
Never mind. It was stupid question.
I think I got the answer.
 

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

Why is Monte Carlo used for calculating the VEV?

The VEV, or vacuum expectation value, is a key concept in quantum field theory and is used to calculate physical quantities. Monte Carlo methods involve using random numbers to simulate a large number of possible outcomes, making it an efficient and accurate way to calculate the VEV.

How does Monte Carlo help with calculating the VEV?

Monte Carlo methods use repeated random sampling to approximate the VEV, taking into account all possible outcomes. This allows for a more accurate and efficient calculation compared to traditional methods, which can be limited by the complexity of the system being analyzed.

Can Monte Carlo be used for any type of system to calculate the VEV?

Yes, Monte Carlo methods can be applied to a wide range of systems, including simple and complex ones, to calculate the VEV. It is a versatile and powerful tool that is widely used in various fields of science and engineering.

What are the advantages of using Monte Carlo for calculating the VEV?

Monte Carlo methods allow for the calculation of the VEV without the need for analytical or numerical solutions, which can be time-consuming and challenging for complex systems. It also provides a more accurate result by taking into account all possible outcomes.

Are there any limitations to using Monte Carlo for calculating the VEV?

While Monte Carlo methods are powerful and versatile, they do have some limitations. They can be computationally expensive for very large systems, and the accuracy of the result can be affected by the quality of the random numbers used. Additionally, certain types of systems may not be well-suited for Monte Carlo methods.

Similar threads

QFT on the lattice and Green's functions
Replies
1
Views
1K
A Monte Carlo to compute uncertainties, why report the mean and SD?
Replies
2
Views
1K
Using Monte Carlo simulation to calculate Value At Risk
Replies
1
Views
5K
Uncertainty calculation for calculating pi using Monte Carlo integration
Replies
5
Views
6K
A Calculating higher order terms for Electron Anomalous Magnetic Moment
Replies
6
Views
762
I Why Monte Carlo Simulations? What do they tell us?
Replies
9
Views
2K
How to Calculate Correlation Time Using Numpy for Monte Carlo Simulations?
Replies
1
Views
2K
Why Does Multiplying by 20 Correct My Monte Carlo Integration Result?
Replies
1
Views
1K
A Least-squares calculation with a pinch of weights and monte-carlo
Replies
2
Views
1K
Python Monte Carlo error calculation PYTHON
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top