Wolves, rabbits and quantum field theory
If you're in Oxford tomorrow - Tuesday March 4 - check out my talk on Fock space techniques for stochastic physics
. It'll be in the Quantum Field Theory seminar at 12 noon in Lecture Room 5 in the Mathematics Institute.
The idea is that random processes involving large objects can be studied by slightly tweaking the math we use to describe elementary particles! Here, for example, is a Feynman diagram involving rabbits and wolves.
Now in case you're wondering: I do know that rabbits engage in sex
, so it's not really true
that rabbits reproduce as shown in this picture. Similarly, it's not really true
that a lone wolf eats a rabbit and suddenly has a baby wolf. This example is just for fun! There are other more serious examples!
But amusingly, if you take this oversimplified model and turn the crank, you get - in the limit of large numbers of rabbits and wolves - the famous Lotka-Volterra equations
describing how the populations of predators and prey change with time. And before we take that limit, we get a more complicated model describing how the probability of having any number of predators and prey changes with time. This is called a stochastic
model because it involves randomness.
And the real point of my talk will not be rabbits and wolves - it will be how we can take math used to describe the change of 'amplitudes' in quantum systems, and rework it to describe the change of probabilities in stochastic systems. Stuff like 'annihilation and creation operators' on 'Fock space', beloved by particle physicists, can be reused in this very different context, and it still works!
If you can't go to the talk, you can still see the slides here:http://math.ucr.edu/home/baez/networks_oxford/Fock_space.pdf