# 6805: 1094 Activities 12

Write your name and answers on this sheet and hand it in at the end.

## Follow-up questions on QCD

Goal: Check understanding of some fundamental ideas of QCD and how it is studied.

1. Why is the QED interaction screened while the QCD interaction is anti-screened?

2. What is gained by studying QCD at ever higher-energy particle accelerators?

3. How would you briefly define (or explain) asymptotic freedom and confinement?

## Path integrals, Part 2

Goal: Understand the basics of path integrals using a quantum mechanics example. In this second part, we try out the Metropolis algorithm.

1. Open the Mathematica notebook path_integral_qm_part2.nb. The top part is just a repeat of section 3 from Part 1, "Propagator as a path integral". Run this section and check that it gives similar results to before. What is a "path" here? How do we "sum over paths"?

2. Random numbers from Mathematica.
1. The Metropolis algorithm will generate a series of paths, and to get each new one we need random numbers that tell us how to change the value of x at each discrete time point. In the notebook, you first generate a table of 100 random numbers and plot them. Do they look random? Why do you say yes or no?

2. Next we make an x-y plot of 100 pairs of random numbers. What do you look for here? Then try 1000 pairs and finally 10000 pairs. Do the 10000 pairs 5 to 10 times. Is it perfectly uniform? Does it look random? Why?

3. Metropolis for ground-state energy.
1. Do the first part of section 5 step-by-step through "Ok, let's try it by hand at first". When running update right after initialize, did all the numbers change from 0? Why do some change and others don't?

2. Now run the last part ("Let's put the entire plan together"). Did it give a good answer for the ground state? What if you increase Nconfig?

3. What questions do you have about the Mathematica implementation?