About Feynman diagrams: it is really SICK how precise and exact they can be. I believe the hidden symmetries of role in QFT are yet to be fully unveiled. In fact, there are some works relating Feynman graphs with number theory (to be more precise, polylogarithms, elliptic polylogarithms and other strange generalized functions; that the Apery constant appears indeed in recent works related to that, and with connections to the amplituhedron and similar structures, not only with string amplitudes, reveal a yet to uncover relationship between number theory, algebraic geometry and the physics of amplitudes of high energy physics that stumbles me so much as its complexity, beauty and …order). However, I admit myself to be a complete nut about the new research on periods of feynman graphs in QFT. I am yet expecting a good review paper to upgrade my knowledge of that subject…The Riemann Hypothesis also waits for such development (I think the proof of RH could also involve some hint of connections not only with Dirichlet L-functions, but also with the structure of QFT and Feynman graphs). Maybe this century and the following will develop abstract algebraic structures to be used in the TOE. I feel non-archimedian analysis could be playing a higher role in physics at the end point…However, I am not updraded of p-adic QFT studies in holography that I really want to read this Christmas…

]]>Great! You can also try ignoring the formulas and reading the words. Maybe that’s unpleasant, but most of the time I try to say everything in words; the equations are supposed to say the same thing a bit more precisely.

]]>You have to love it, or it makes you angry.

I would like to understand those numbers! There’s a lot of interesting number theory hiding in the evaluation of Feynman diagrams.

John Donoghue and coauthors computed the quantum corrections to the potential for gravity using perturbative quantum gravity and got

The first correction is due to general relativity; the next one is really a quantum gravity effect.

]]>Sometime I should check those out!

]]>I believe Weinberg just proposed a simple framework to describe small deviations from linearity in (some applications of) quantum mechanics, a bit like how the parametrized post-Newtonian formalism lets us describe small deviations from Newtonian gravity, so we can organize experiments to compare general relativity against other theories. But this is just my impression—I’ve never studied his work! I’m pretty sure neither he nor Penrose came up with a detailed theory describing small nonlinear deviations from quantum mechanics.

If an expert on this subject reads this, please chime in!

]]>photon+photon -> matter

which was only observed in the last few years:

]]>Sounds like one of those (then) new southern-California religions back in the 1960s founded by someone who, in the words of Kirk, took too much LDS.

]]>Is that related to Penrose‘s ideas about gravity affecting quantum mechanics?

Penrose has done some excellent stuff: singularity theorems, irregular tiling, and so on. His latest cosmology speculations haven‘t really convinced many, and hardly anyone believes in his quantum-consciousness stuff.

But his gravity-could-affect-quantum-mechanics stuff seems reasonable, at least at first glance. I suspect that most suspect that GR but perhaps not QM will have to be modified for quantum gravity.

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