Question
An infinite dimensional generalization of an equation named after this man gives the time evolution of a probability measure in terms of a Euclidean inner product. For 10 points each:
[10h] Name this physicist. The Lie (“lee”) derivative of the symplectic structure along a vector field equals zero according to a result named after this physicist.
ANSWER: Joseph Liouville [accept Liouville’s theorem or Liouville equation or Liouville’s equation]
[10m] This operation appears in some versions of Liouville’s equation. This classical analogue of the commutator is denoted using curly brackets.
ANSWER: Poisson bracket
[10e] The Poisson bracket of canonical momentum and position is formally given by one of these functions named after Kronecker. These functions take their name from a Greek letter, and one of these functions named after Dirac nominally equals infinity at zero and equals zero everywhere else.
ANSWER: delta functions [accept Kronecker delta function or Dirac delta function or Dirac delta distribution]
<Physics>
Summary
| 2025 ACF Nationals | 04/19/2025 | Y | 12 | 20.00 | 100% | 83% | 17% |
Data
| Penn State | Chicago B | 0 | 10 | 10 | 20 |
| Minnesota | Columbia A | 0 | 0 | 10 | 10 |
| Columbia B | Arizona State | 0 | 10 | 10 | 20 |
| MIT | Illinois B | 0 | 10 | 10 | 20 |
| Indiana | Yale | 10 | 10 | 10 | 30 |
| Northwestern | Johns Hopkins | 0 | 10 | 10 | 20 |
| Ottawa | North Carolina A | 0 | 10 | 10 | 20 |
| Georgia Tech | North Carolina B | 10 | 0 | 10 | 20 |
| Stanford | UCF | 0 | 10 | 10 | 20 |
| WUSTL A | Cornell B | 0 | 10 | 10 | 20 |
| Cornell A | Waterloo A | 0 | 10 | 10 | 20 |
| Waterloo B | UC Berkeley A | 0 | 10 | 10 | 20 |