Recent content by Jim Kata

Globally it is not invariant, as you have shown, but I believe locally it is invariant under conformal transformations. This is probably nothing special per se since the EH action is, modulo a total derivative, invariant under all gauge transformations. For all transformations of the form...

The problem is this: Paraphrasing Polchinski from String Theory volume 1 "A number of familiar field theories in four dimensions are classically invariant under rescaling, pure Yang-Mills, \phi^{4} and so on. However, we know that due to divergences in the quantum theory, there is a nonzero...

What does the existence of the Weyl curvature tensor have to do with the conformal-covariance, or not, of a gravitational theory on a Riemannian spacetime? Please be specific in your answer, preferably with math. What I mean by conformal invariance in equations is the following: Given the...

Here's my sketch of a solution. Quoting Weinberg volume 1 again : "Although non-renormalizable theories involve an infinite number of free parameters, they retain considerable predictive power. They allow us to calculate the non-analytic parts of Feynman amplitudes, like the In q and q In q...

Since you're so fond of quoting Wikipedia, here's a quote directly from Wikipedia on the Weyl Curvature tensor page. "In general relativity, the Weyl curvature is the only part of the curvature that exists in free space—a solution of the vacuum Einstein equation—and it governs the propagation...

To answer your question about citation I am quoting Penrose and Rindler volume 1 page 240. Here is a paraphrase of the quote : "The tensor C_abcd is called the Weyl conformal tensor ( and Psi_abcd is often called the Weyl conformal spinor). It comprises the conformally invariant part of the...

In reading Weinberg volume 1 I learned gravity is not renormalizable by Dyson power counting. This means that it has an infinite number of free parameters, and such theories lose their predictive power at energies of the common mass scale. This being said, T Hooft and Veltman showed miraculously...

Thank you everyone for your thoughtful responses. I would like to drill down on something Mitchell Porter said: "The CFT stress-energy tensor, at a particular point on the boundary, is holographically equivalent to the emission of a graviton into the emergent AdS space from that point (emergent...

The graviton is the helicity two particle one gets when quantizing gravity in a metric formulation. There are two reasons why I have this question. 1.) If you formulate gravity in a tetrad formulation you don't seem to have a helicity two particle just the tetrad and the connection which both...

Consider the following thought experiment, two electrons are in an entangled state with a total angular momentum of zero. They split apart from each other some billion or so years ago and I observe one of the electrons right now. Before the observation, there is some probability that it will be...

Thank you for your answer mathwonk. It seems to work.

Is it true that if two functors are adjoint, then their derived category functors are adjoint? I'm thinking in particular of ext^n and tor_n. The answer seems like it would be obviously yes to me, but I don't think I've seen it spelled out, and I am too lazy to try and prove it. Is there a...

It's chapter fifteen of volume II. I should note that Green, Schwarz, Witten and Griffiths and Harris come at the subject from more of a topology of complex manifolds standpoint, which in imo is more useful to a physicist, and the Chapter in Dummit and Foote and Hartsthorne come at it from...

In Green, Schwarz, Witten volume 2, they have a chapter on Algebraic Geometry that I found to be very accessible. There is a nice introductory chapter to algebraic geometry in Dummit and Foote too. As far as full books on the subject are concerned, I agree with the the recommendation of...

Just rambling, but what would fascinate me is if the 3 generations of particles in the standard model could be explained by those 3 copies of E_8 in the off diagonal terms in h_3(O).