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

Work with others at your table on these activities. Argue about the answers but work efficiently!

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

*Why is the QED interaction screened while the QCD interaction is anti-screened?*

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

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

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

- 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"?*

**Random numbers from Mathematica.**- 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?*

- 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?*

- 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.
**Metropolis for ground-state energy.**- 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?*

- 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?*

- What questions do you have about the Mathematica implementation?

- Do the first part of section 5 step-by-step through "Ok, let's
try it by hand at first".

furnstahl.1@osu.edu