Quantum Field Theory (QFT), General Relativity (GR), and Other Exciting Diversions (OED)

Posted on 02/11/2011

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Classification of Lie Groups

QFT

ResearchBlogging.org

Classification of Lie Groups

classification of Lie groups

I’m lucky to have a job in which I can take two weeks of mornings of work to study a nominally tangential subject in greater depth. These past two weeks I attended a series of  lectures at the ETH on physics beyond the standard model, the first week was very technical but exciting to me as a non-specialist, an introduction to composite-Higgs models for electroweak symmetry breaking. The second week was on much more familiar territory,  how physics beyond the standard model can emerge in astrophysics and cosmology, but as a consequence a little less exciting to me. The curse of the compulsively curious is that we are always most interested in that which we understand least.

Prior to the lectures I spent my mornings reading up on QFT. I’ve audited an introductory QFT course and have a solid foundation in quantum mechanics, linear algebra, group theory and differential geometry so my readings with a few calculations were approachable. Nevertheless I still have a lot to learn about the subject and as it’s not my primary research focus I’m taking it slow. I’m going to audit the advanced level QFT course next semester and hopefully by the end of my PhD I’ll be able to follow the latest results from theorists and the LHC with an even greater appreciation and wrestle with modern developments in string theory or whatever may come next.

Some readings I found particularly helpful:

GR

I also attend meetings of gr-qc, a general relativity and quantum cosmology reading group. Today we discussed a paper which claims to resolve galactic rotation without resorting to dark matter, one of a series which began in 20052.. It doesn’t address any of the other evidence for dark matter, including lensing data, but is an interesting theoretical argument. The authors begin with a stationary axially symmetric metric then consider the Einstein field equations. From these they derive Laplace’s equation as a function of the angular and tangential velocities, which are themselves a function of r and an as yet specified parameter N(r,z) which appears in the metric. The solutions of this in cylindrical coordinates are Bessel functions, and fixing the coefficients of the Bessel functions amounts to fixing a particular N.

From this N and the field equations, we can infer the density distribution and the angular and tangential velocities. If these match observations, which the authors claim they do, then we have explained the rotation curves without the need to resort to dark matter. There are several papers in the series and we didn’t have time to discuss them in depth along with rebuttals and criticism–all of us are rather skeptical of various stages of the calculation and of the way the results were compared with observations. Nevertheless this paper provided an interesting concept and approach and was worth a read.

OED

One of my philosophies of productivity and in fact life is when I get obsessively interested in something, no matter how tangential it may seem, to follow it. I call this my “never turn down a free train ticket principle. I can’t entirely predict when, where, what and why but I have bouts of obsession and when I follow one I get a free ride to an interesting place, which if I’m lucky is filled with fantastic conceptual scenery. Eventually I have to take the train back to work, especially if I have a deadline looming. So boarding, now; luckily the trains back to work run on a regular schedule.

Citations

1. M. Robinson, K. Bland, G. Cleaver, & J. Dittmann (2008). A Simple Introduction to Particle Physics ArXiv arXiv: 0810.3328v1
2. F. I. Cooperstock, & S. Tieu (2005). General Relativity Resolves Galactic Rotation Without Exotic Dark Matter arXiv arXiv: astro-ph/0507619v1

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