Standard Model at the horizon


Hawking radiation is one of the most famous effects where quantum field theory combines successfully with general relativity. Since 1975 when Stephen Hawking uncovered it, this result has obtained a enormousStephen Hawking consideration and has been derived in a lot of different ways. The idea is that, very near the horizon of a black hole, a pair of particles can be produced one of which falls into the hole and the other escapes to infinity and is seen as emitted radiation. The overall effect is to drain energy from the hole, as the pair is formed at its expenses, and its ultimate fate is to evaporate. The distribution of this radiation is practically thermal and a temperature and an entropy can be attached to the black hole. The entropy is proportional to the area of the black hole computed at the horizon, as also postulated by Jacob Bekenstein, and so, it can only increase. Thermodynamics applies to black holes as well. Since then, the quest to understand the microscopic origin of such an entropy has seen a huge literature production with the notable Jacob Bekensteinunderstanding coming from string theory and loop quantum gravity.

In all the derivations of this effect people generally assumes that the particles are free and there are very good reasons to do so. In this way the theory is easier to manage and quantum field theory on curved spaces yields definite results. The wave equation is separable and exactly solvable (see here and here). For a scalar field, if you had a self-interaction term you are immediately in trouble. Notwithstanding this, in  the ’80 UnruhWilliam Unruh and Leahy, considering the simplified case of two dimensions and Schwarzschild geometry, uncovered a peculiar effect: At the horizon of the black the interaction appears to be switched off (see here). This means that the original derivation by Black-hole-model by Kip ThorneHawking for free particles has indeed a general meaning but, the worst conclusion, all particles become non interacting and massless at the horizon when one considers the Standard Model! Cooper will have very bad times crossing Gargantua’s horizon.

Turning back from science fiction to reality, this problem stood forgotten for all this time and nobody studied this fact too much. The reason is that the vacuum in a curved space-time is not trivial, as firstly noted by Hawking, and mostly so when particles interact. Simply, people has increasing difficulties to manage the theory that is already complicated in its simplest form. Algebraic quantum field theory provides a rigorous approach to this (e.g. see here). These authors consider an interacting theory with a \varphi^3 term but do perturbation theory (small self-interaction) probably hiding in this way the Unruh-Leahy effectValter Moretti.

The situation can change radically if one has exact solutions. A \varphi^4 classical theory can be indeed solved exactly and one can make it manageable (see here). A full quantum field theory can be developed in the strong self-interaction limit (see here) and so, Unruh-Leahy effect can be accounted for. I did so and then, I have got the same conclusion for the Kerr black hole (the one of Interstellar) in four dimensions (see here). This can have devastating implications for the Standard Model of particle physics. The reason is that, if Higgs field is switched off at the horizon, all the particles will lose their masses and electroweak symmetry will be recovered. Besides, further analysis will be necessary also for Yang-Mills fields and I suspect that also in this case the same conclusion has to hold. So, the Unruh-Leahy effect seems to be on the same footing and importance of the Hawking radiation. A deep understanding of it would be needed starting from quantum gravity. It is a holy grail, the switch-off of all couplings, kind of.

Further analysis is needed to get a confirmation of it. But now, I am somewhat more scared to cross a horizon.

V. B. Bezerra, H. S. Vieira, & André A. Costa (2013). The Klein-Gordon equation in the spacetime of a charged and rotating black hole Class. Quantum Grav. 31 (2014) 045003 arXiv: 1312.4823v1

H. S. Vieira, V. B. Bezerra, & C. R. Muniz (2014). Exact solutions of the Klein-Gordon equation in the Kerr-Newman background and Hawking radiation Annals of Physics 350 (2014) 14-28 arXiv: 1401.5397v4

Leahy, D., & Unruh, W. (1983). Effects of a λΦ4 interaction on black-hole evaporation in two dimensions Physical Review D, 28 (4), 694-702 DOI: 10.1103/PhysRevD.28.694

Giovanni Collini, Valter Moretti, & Nicola Pinamonti (2013). Tunnelling black-hole radiation with $φ^3$ self-interaction: one-loop computation for Rindler Killing horizons Lett. Math. Phys. 104 (2014) 217-232 arXiv: 1302.5253v4

Marco Frasca (2009). Exact solutions of classical scalar field equations J.Nonlin.Math.Phys.18:291-297,2011 arXiv: 0907.4053v2

Marco Frasca (2013). Scalar field theory in the strong self-interaction limit Eur. Phys. J. C (2014) 74:2929 arXiv: 1306.6530v5

Marco Frasca (2014). Hawking radiation and interacting fields arXiv arXiv: 1412.1955v1

Back to work


Today I am back in my office and physics, that I never stopped to think of, is unfriendly urging in my mind. Besides my work as a reviewer for Mathematical Reviews that I try to do at my best, I have not forgotten to look around in the blogosphere. In these days there is a lot of fuss about a recent paper by Fermi Collaboration (see here). You can find some discussion here but it is not the only blog discussing this matter: An inflamed discussion is also here. Is loop quantum gravity dead? I can only spend a few words here by saying that is really too early to draw such conclusions but the results from Fermi Collaboration are really beautiful and open the premises for a bright future in the observation of gamma ray bursts. I would like to remember here the point of view of Steven Weinberg claiming that we finally hit exact truths on Nature (the bitch not the journal as  Tommaso Dorigo uses to say ). These truths are special relativity and quantum mechanics. I share this idea and the more beautiful idea that we are indeed able to reach such exact truths, the same mathematicians are able to achieve. On the same ground, if some experiment should come out claiming that these theories should be modified, I would be glad for one thing: A great opportunity for my generation to put hands on a deeper truth.

I am still working on a perturbation analysis of a non-perturbative Higgs field interacting with a fermion. I am solving Heisenberg equations of motion with a very large coupling for the Higgs. I hope to get some further time to complete the computations that may become really involved.

About QCD there is few to say. I have got my paper accepted for publication as you may know that implied a nice correspondence with Terry Tao. We can say that, after the very good Terry’s intervention, the proof of the mapping theorem is indeed complete. Another paper hit my interest and arose from a Japanese group working on lattice (see here). I have had an email exachange with Hideo Suganuma and surely their results are something to think about in depth. I hope to see other papers in the near future as this area of physics is very active indeed.

Finally, great expectations are for LHC. It will start on November and we hope to see results very soon. Infancy problems should be overcome and it is time to see the face of Higgs (the particle not the professor). Good luck, folks!

QuAD constrains parity violation on a cosmic scale


QuAD is a collaboration that involves several institutions that aims to measure polarization of photons of the Cosmic Microwave Background radiation that is the relic radiation that started to freely propagating in the universe 400000 years after big bang. QuAD aerialThis radiation is a precious source of information for a deeper understanding of the birth of our universe and a fundamental test-bed for our theories. This collaboration proved that our “standard model” of the universe again agrees with their measurement about polarization of this radiation. But, from these data, physicists are able to get something more. In a paper appeared in the last number of PRL (see here and here), they showed that electrodynamic forces are proved to not violate parity on a cosmic scale and, last but not least, interactions that violate Lorentz invariance are strongly constrained.

I should say that this is an important conclusion to be drawn from an elegant experiment and an unexpected source.

Evidence for dark matter from PAMELA


Two lines to point out this paper, appeared in the latest number of Nature, coming from PAMELA Collaboration. This project is directed by Piergiorgio Picozza. He has been my professor of nuclear physics at Rome University La Sapienza (but all my mistakes about are my own responsability…). pamelaPAMELA is a satellite that is orbiting Earth since 1023 days to date (you can find a counter on PAMELA’s site) and is gathering data about cosmic radiation. They have found an enhanced production of positrons. In this last paper they reach the relevant conclusion that this excess may come from dark matter through an annihilation process. This appears a significant evidence for the existence of this exotic matter that we expect to be produced at LHC in the next months as the consequences of the accident happened last year will be definitively fixed. Let me say that I find PAMELA exceedingly sexy as what she is saying to us is really exciting.

Most extreme gamma-ray blast yet


As my blog’s readers know, I follow as far as I can space missions that can have a deep impact on our knowledge of universe. Most of them are from NASA. One of these missions is Fermi-GLAST that has produced a beautiful result quite recently.  glastIt has seen the greatest gamma-ray burst ever (see here). The paper with the results is appeared on Science (see here). The burst was seen in Carina constellation.  These explosions are the most energetic processes in the universe and were uncovered by chance with military satellites named Vela used to find nuclear explosions in the atmosphere in the sixties of the last century. Understanding gamma-ray bursts implies a deeper understanding of stellar explosions.


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