Domenic Denicola . com
Webmaster, student, thinker
The following is an edited version of a report I submitted to the Perimeter Institute administrators on the work I did under the supervision of Samuel Colin and Ward Struyve.
We started out by looking into Ward and Samuel's Dirac sea pilot-wave model for quantum field theory, with the intention of attempting to introduce basic interactions into a course-grained version that would help show that it reproduced quantum predictions. After that began to look intractable, we became interested in Bohmian trajectories for the Dirac-sea particles. I worked through the results algebraically, and wrote up a Mathematica simulation using this knowledge. The simulation provided some very interesting results, the most intriguing of which was that the particles in the Dirac sea appear to have zero velocity. This was verified analytically for small numbers of particles, and we are currently attempting to prove it for the general case.
In addition, Ward gave me an interesting project to work on while we were stuck on the aforementioned proof. He showed me a pilot-wave quantum field theory model by Holland that used a trio of angles at each point [parameterizing SU(2)] to create a fermionic pilot-wave quantum field theory. Holland's model was formulated in momentum space, which provides no usable ontology; associating a trio of angles to each possible momenta is not something one can readily make sense out of in terms of the actual world. My task was to reformulate it in position space. I did so, producing a continuity equation for the position-space model. Once that was finished we determined that we needed to see if the position-space model reproduced quantum predictions. Although there were some interesting results, such as indicating that this trio of angles had one orientation for particle-filled lattice sites and another for vacuum lattice sites, in the end the fact that particle states were so sparse in a typical macroscopic system made it clear that two macroscopic states would not be distinguishable unless they were each much larger than the visible universe, which is quite unrealistic. Thus, we gave up on the position-space translation of Holland's model.
With regards to publications, we are hoping to publish one on the analysis of trajectories in the Dirac sea pilot-wave model of Ward and Samuel. This is still work in progress. The result so far obtained on Holland's model should also appear in a paper. However, because of the nature of the result, it is as yet unclear whether it should be included in Ward's paper, or whether it should be published separately. This will in part depend on the results that related avenues lead to.
To model the Bohmian trajectories of the Dirac sea particles, I implemented a portion of the formalism of quantum field theory in Mathematica. With the relativistic Bohmian guidance equation (as per Ward and Samuel’s paper), Mathematica’s native numerical differential equation solving capabilities allowed us to plot the trajectories of any finite set of particles, specifying arbitrary initial positions, momenta, and spins.
As noted on my résumé, I am fluent in several operating systems and programming environments, and have done both general programming and simulation work for fun in addition to the above. Moreover, I consider myself quite capable of learning new systems and languages as appropriate for the job; indeed, if you were to give me advance notice I could easily do so ahead of time, while primarily engaging in other projects. That said, I prefer theorizing to modeling if possible.