Time for a second blog post. I will readily admit we have been a bit slow with the blog. There have been a lot of new developments in the interim. Things that Have prevented us from doing too much here, but we are trying to change that. We have a basecamp now, and we are actually divvying up tasks and setting due dates. There will be some hits and misses as we try and get our new podcast off the ground -- likely some ugly moments -- but that all needs to happen. That will be posted here as soon as it is ready and I will share some more personal updates in the meantime.
I am now in my second year of a physics PhD program. As a second year graduate student, I am starting to feel like I actually am a research physicist. Before tackling my physics life, I'll tell you some happenings in my life. My S.O.and I moved apartments and were able to rent without a guarantor--something that felt like a major adult milestone. I have been biking to work of late. According to the vlogbrothers, that puts me among the happiest of commuters: One Scientifically Proven Thing Actually Makes People Happier. I do not know if I would agree during the ride, but there is a certain satisfaction in arriving.
I spent the summer working with scalar Quantum Field Theories on the lattice. Specifically, I have been examining Phi4 theory. For those of you interested, I refer you to Peskin and Schroeder, as well as Rothe: Lattice Gauge Theories. For those of you looking only for a flavor, let me explain a bit further. A scalar field theory can be best described as the field theory describing a gas of bosons. Instead of treating these bosons as particles, we treat them as disturbances within a field that spans all the spatial dimensions as well as time. The dynamics of the field are contained within the Feynman Path Integral formalism.
The path integral can be thought of as an integral over all possible field configurations with each path weighted by a complex exponential of the action. The complex exponential makes calculating the results of the path integral difficult because it is hard to determine which paths contribute to the integral and which paths are suppressed (a complex exponential can be expanded into cos(x)+i*sin(x) where i is the \sqrt{-1}).
In lattice field theory, we get around this by converting our time variable into something called imaginary time or t-> i*t, this conversion removes the complex portion of the exponential (It also moves us out of our standard Minkowski space, which is the metric space that Relativity needs to function, but that is neither here nor there at the moment...). This new path integral is called the Euclidean path integral and the action the Euclidean action. With the decaying exponential, we can now use analytic methods to calculate the observables of a free particle, but the integral cannot be solved analytically in most cases.
For those, we use what is a Metropolis Monte Carlo algorithm. I am currently working on a write-up that describes this in detail. Until that time, know that the general idea is that we select paths with a probability based on the distribution defined by the decaying exponential in the path integral. There are additional complications when dealing with fermions, but the scalar field case is useful because it allows us to explore new methods for implementing the Monte Carlo on something that is not computationally intractable, and can be solved through other means.
This post has already been rambling for quite some time, so I will cut the QFT discussion of there. I did explore additional aspects of simulating the path integral, but those are still active areas of my research, and needs to be explored further. I will quickly mention my other project, which is modeling Gamma Ray Bursts by scaling shockwave models to determine physical parameters of the shockwave based on key frequencies and fluxes in their spectrum, but I have only been on this project about a week.
Look for more updates on all of these topics, as well as our first podcast, by mid-October.
Cheers,
TEJ
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