## Lucasian chair again

13/02/2013

On 22 May, Professor Michael Green, the incumbent Lucasian Professor at Cambridge University, will be 67 and must retire. He succeeded Stephen Hawking that left this chair for the same reason on 2009. Well before Hawking’s retirement, Cambridge University issued an announcement asking for possible candidates and, after the selection ended, Professor Green come out as the chosen one. This time, no announcement is out from Cambridge and so, it is possible that the successor of Professor Green should be already known. I think the news will be released in the next few months. Till now, no rumors spread.

## Back to CUDA

11/02/2013

It is about two years ago when I wrote my last post about CUDA technology by NVIDIA (see here). At that time I added two new graphic cards to my PC, being on the verge to reach 3 Tflops in single precision for lattice computations.  Indeed, I have had an unlucky turn of events and these cards went back to the seller as they were not working properly and I was completely refunded. Meantime, also the motherboard failed and the hardware was largely changed  and so, I have been for a lot of time without the opportunity to work with CUDA and performing intensive computations as I planned. As it is well-known, one can find a lot of software exploiting this excellent technology provided by NVIDIA and, during these years, it has been spreading largely, both in academia and industry, making life of researchers a lot easier. Personally, I am using it also at my workplace and it is really exciting to have such a computational capability at your hand at a really affordable price.

Now, I am newly able to equip my personal computer at home with a powerful Tesla card. Some of these cards are currently dismissed as they are at the end of activity, due to upgrades of more modern ones, and so can be found at a really small price in bid sites like ebay. So, I bought a Tesla M1060 for about 200 euros. As the name says, this card has not been conceived for a personal computer but rather for servers produced by some OEMs. This can also be realized when we look at the card and see a passive cooler. This means that the card should have a proper physical dimension to enter into a server while the active dissipation through fans should be eventually provided by the server itself. Indeed, I added an 80mm Enermax fan to my chassis (also Enermax Enlobal)  to be granted that the motherboard temperature does not reach too high values. My motherboard is an ASUS P8P67 Deluxe. This is  a very good card, as usual for ASUS, providing three PCIe 2.0 slots and, in principle, one can add up to three video cards together. But if you have a couple of NVIDIA cards in SLI configuration, the slots work at x8. A single video card will work at x16.  Of course, if you plan to work with these configurations, you will need a proper PSU. I have a Cooler Master Silent Pro Gold 1000 W and I am well beyond my needs. This is what remains from my preceding configuration and is performing really well. I have also changed my CPU being this now an Intel i3-2125 with two cores at 3.30 GHz and 3Mb Cache. Finally, I added  16 Gb of Corsair Vengeance DDR3 RAM.

The installation of the card went really smooth and I have got it up and running in a few minutes on Windows 8 Pro 64 Bit,  after the installation of the proper drivers. I checked with Matlab 2011b and PGI compilers with CUDA Toolkit 5.0 properly installed. All worked fine. I would like to spend a few words about PGI compilers that are realized by The Portland Group. I have got a trial license at home and tested them while at my workplace we have a fully working license. These compilers make the realization of accelerated CUDA code absolutely easy. All you need is to insert into your C or Fortran code some preprocessing directives. I have executed some performance tests and the gain is really impressive without ever writing a single line of CUDA code. These compilers can be easily introduced into Matlab to yield mex-files or S-functions even if they are not yet supported by Mathworks (they should!) and also this I have verified without too much difficulty both for C and Fortran.

Finally, I would like to give you an idea on the way I will use CUDA technology for my aims. What I am doing right now is porting some good code for the scalar field and I would like to use it in the limit of large self-interaction to derive the spectrum of the theory. It is well-known that if you take the limit of the self-interaction going to infinity you recover the Ising model. But I would like to see what happens with intermediate but large values as I was not able to get any hint from literature on this, notwithstanding this is the workhorse for any people doing lattice computations. What seems to matter today is to show triviality at four dimensions, a well-acquired evidence. As soon as the accelerate code will run properly, I plan to share it here as it is very easy to get good code to do lattice QCD but it is very difficult to get good code for scalar field theory as well. Stay tuned!

## Fabiola Gianotti at Accademia dei Lincei

11/01/2013

On November 7th last year, Fabiola Gianotti, spokesperson of ATLAS experiment at CERN and one of the discoverers of the Higgs-like boson, has been nominated fellow of the Accademia dei Lincei. This is one of the oldest and most prestigious scientific societies that held fellows like Galileo Galilei and Enrico Fermi. Today, she held a public conference with fellows both of moral and scientific classes about “The Higgs boson and our life”. Of course, I was there to see and listen to her personally. As I entered the room, I asked “excuse me” to three people blocking my passage to the chair. When I sat, I looked at them and I realized who were: Carlo di Castro, Francesco de Martini and Giovanni Jona-Lasinio. They were all my former professors. Also Giorgio Parisi was there and later Luciano Maiani entered the audience. Undoubtedly, the audience was truly remarkable.

Lamberto Maffei, president of the Accademia, introduced Gianotti through her main achievements and awards. I would like to remember that she gave the money of the Fundamental Physics Prize for student grants.

The aim of this conference was to convey to all fellows of the Accademia and public at large what was behind the discovery of the Higgs-like particle announced on July 4th last year. For me has been a good chance to hear, from one of the persons mastering this matter, a talk addressed to everybody without the use of technical jargon and using several nice images. Gianotti has shown a very fine gift for this. I would like to reassure my readers that she used comic sans.

By my side, I was proud to hear that 1400 scientists working at CERN are Italians and that an Italian company, Ansaldo Superconduttori Genova, is responsible for one third of the realization of the superconductors at LHC and are also installed in ATLAS detector. At CERN it is working  a great majority of young people. Gianotti said that it does not matter if you are a graduate student just entered the team. If your idea is good it is taken and applied. This is what makes scientific enterprise quite different from other realities and renders it so effective. Ideas count more than any authority.

Gianotti pointed out how difficult the situation is for Italy as we have a lot of young people leaving the country for academic positions at foreign universities while there are very few students coming in Italy to do research. Also, reduced budgets from our government with nonsensical cuts can produce a gap between generations of a line that produced excellent people. Recovering would be difficult then.

Turning attention to the discovery, I would like to emphasize that Gianotti repeated more and more times that the only certainty is that Standard Model, a beautiful theory, is verified with very high precision without no hint of breaking so far. But she warned the audience that we know that it must be overcome motivating this mostly from evidence of dark matter. The new particle, she said “Higgs-like”, resemble more and more the one originally postulated by Peter Higgs et al. but they have a lot of data to analyse yet and cannot be certain it is that one yet. They hope to clarify this matter with these other data (Moriond?). She used an interesting image to describe the Higgs field to common people and then turned to the technical one to recover with respect to the formidable physicists were present there. Who speaks Italian can appreciate this video: Gianotti, Tonelli and Bertolucci explain Higgs field with children on similar lines.

The reason why she referred to our life is that most people generally ask “Why?”. Why all this effort to catch such a particle? She gave the beautiful example of J. J. Thompson and the discovery of the electron. When this happened both Thompson’s life and that of his neighbourhood did not change at all. But with the discovery of electronics and its application we all know now what all that has meant. For the Higgs particle can happen the same. From the discovery to its possible applications can pass some time and we need fundamental physics as a priori we cannot foresee the consequences but when they appear can be devastating and change our life definitely and forever for better. Gianotti said that without fundamental research, applied research dries up and eventually dies causing serious troubles to the economy of a country. I completely share her view. She also showed how hadron therapy and pet imaging were by-products of such endeavour.

Questions took more time than expected as the talk was really exciting and several people asked questions. She took this chance to recognize her debt with Ettore Fiorini, in the audience, that introduced her to particle physics and taught her a lot about it. Also Giorgio Salvini was present and asked for beyond LHC. Gianotti said that they hope to have LHC running for more than twenty years as also happened to other accelerator facilities. Salvini participated to most of the history of particle physics since Fermi’s time. He was in the experiment at CERN that produced W and Z particles for the first time with Carlo Rubbia. Francesco de Martini asked a technical question: Has Higgs particle cosmological implications? He was referring to a paper by Lee Smolin that claims that, due to this field, geometry should change from a Riemann to a Weyl one. Gianotti answered immediately that the cosmological implications for the Higgs particle are enormous. The reason is that this is the first scalar particle ever discovered and inflation, the main mechanism in the Standard Model of cosmology to solve the problem of the homogeneity of the universe, has as a basic ingredient a scalar field. CERN discovery shows once again that the idea of inflation is in the right direction. de Martini was not satisfied with the answer turning back to the Smolin’s paper. Then Gianotti asked support to Giorgio Parisi, Parisi is one of the greatest Italian theoretical physicist, that confirmed Gianotti’s answer and said that, even if he is not an expert in the field of general relativity, people working in this research area have devised everything but the kitchen sink and so he would not be surprised if something like this was conceived.

In the end, a very beautiful talk from a great physicist. I would like to paraphrase what Gianotti said about Higgs and its light mass: Thanks Nature for giving us Gianotti!

## End of the year quote

31/12/2012

“Truth alone will endure, all the rest will be swept away before the tide of time. I must continue to bear testimony to truth even if I am forsaken by all. Mine may today be a voice in the wilderness, but it will be heard when all other voices are silenced, if it is the voice of Truth.”

(Mahatma Gandhi, Basic Education (1951), p. 89.)

## Where does mass come from?

16/12/2012

After CERN’s updates (well recounted here, here and here) producing no real news but just some concern about possible Higgs cloning, I would like to discuss here some mathematical facts about what one should expect about mass generation and why we should not be happy with these results, now coming out on a quarterly basis.

The scenario we are facing so far is one with a boson particle resembling more and more the Higgs particle appearing in the original formulation of the Standard Model. No trace is seen of anything else at higher energies, no evidence of supersymmetry. It appears like no new physics is hiding here rather for it we will have to wait eventually the upgrade of LHC that will start its runs on 2015.

I cannot agree with all of this and this is not the truth at all. The reason to not believe all this is strictly based on theoretical arguments and properties of partial differential equations. We are aware that physicists can be skeptical also about mathematics even if this is unacceptable as mathematics has no other way than being true or false. There is nothing like a half truth but there are a lot of theoretical physicists trusting on it. I have always thought that being skeptical on mathematics is just an excuse to avoid to enter into other work. There could always be the risk that one discovers it is correct and then has to support it.

The point is the scalar field. A strong limitation we have to face when working in quantum field theory is that only small coupling can be managed. No conclusive analysis can be drawn when a coupling is just finite and also lattice computations produce confusion. It seems like small coupling only can exist and all the theory we build are in the hope that nature is benign and yields nothing else than that. For the Higgs field is the same. All our analysis are based on this, the hierarchy problem comes out from this. Just take any of your textbook on which you built your knowledge of this matter and you will promptly realize that nothing else is there. Peschin and Schroeder, in their really excellent book, conclude that strong coupling cannot exist in quantum field theory and the foundation of this argument arises from renormalization group. Nature has only small couplings.

Mathematics, a product of nature, has not just small couplings and nobody can impede a mathematician to take these equations and try to analyze them with a coupling running to infinity. Of course, I did it and somebody else tried to understand this situation and the results make the situation rather embarrassing.

These reflections sprang from a paper appeared yesterday on arxiv (see here). In a de Sitter space there is a natural constant having the dimension of energy and this is the Hubble constant (in natural units). It is an emerging result that a massless scalar field with a quartic interaction in such a space develops a mass. This mass goes like $m^2\propto \sqrt{\lambda}H^2$ being $\lambda$ the coupling coming from the self-interaction and $H$ the Hubble constant. But the authors of this paper are forced to turn to the usual small coupling expansion just singling out the zero mode producing the mass. So, great news but back to the normal.

A self-interacting scalar field has the property to get mass by itself. Generally, such a self-interacting field has a potential in the form $\frac{1}{2}\mu^2\phi^2+\frac{\lambda}{4}\phi^4$ and we can have three cases $\mu^2>0$, $\mu^2=0$ and $\mu^2<0$. In all of them the classical equations of motion have an exact massive free solution (see here and Tao’s Dispersive Wiki) when $\lambda$ is finite. These solutions cannot be recovered by any small coupling expansion unless one is able to resum the infinite terms in the series. The cases with $\mu^2\ne 0$ are interesting in that this term gets a correction depending on $\lambda$ and for the case $\mu^2<0$ one can recover a spectrum with a Goldstone excitation and the exact solution is an oscillating one around a finite value different from zero (it never crosses the zero) as it should be for spontaneous breaking of symmetry. But the mass is going like $\sqrt{\lambda}\Lambda^2$ where now $\Lambda$ is just an integration constant. The same happens in the massless case as one recovers a mass going like $m^2\propto\sqrt{\lambda}\Lambda^2$.  We see the deep analogy with the scalar field in a de Sitter space and these authors are correct in their conclusions.

The point here is that the Higgs mechanism, as has been devised in the sixties, entails all the philosophy of “small coupling and nothing else” and so it incurs in all the possible difficulties, not last the hierarchy problem. A modern view about this matter implies that, also admitting $\mu^2<0$ makes sense, we have to expand around a solution for $\lambda$ finite being this physically meaningful rather than try an expansion for a free field. We are not granted that the latter makes sense at all but is just an educated guess.

What does all this imply for LHC results? Indeed, if we limit all the analysis to the coupling of the Higgs field with the other fields in the Standard Model, this is not the best way to say we have observed a true Higgs particle as the one postulated in the sixties. It is just curious that no other excitation is seen beyond the (eventually cloned) 126 GeV boson seen so far but we have a big desert to very high energies. Because the very nature of the scalar field is to have massive solutions as soon as the self-interaction is taken to be finite, this also means that other excited states must be seen. This simply cannot be the Higgs particle, mathematics is saying no.

M. Beneke, & P. Moch (2012). On “dynamical mass” generation in Euclidean de Sitter space arXiv arXiv: 1212.3058v1

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

## Curiosity finds organics but where do they come from?

04/12/2012

Yesterday, at the meeting of the American Geophysical Union in San Francisco, NASA announced first results from soil analysis performed by Curiosity. Indeed, initially there was an eager expectation about this announcement as some rumors leaked out and somebody told about historical results. Then, all this was teased by NASA but what they announced yesterday was all but disappointing. I followed a real-time chronicle on twitter by Emily Lakdawalla (@elakdawalla and check her blog) that was there in San Francisco and it was really exciting. The main point is that Curiosity indeed has found organics but that people at NASA cannot be sure yet that carbon was not from Earth. Anyhow, the analysis of the soil displayed a rich content and this is indeed a riverbed. Some further analysis are required before to give definitive conclusions about the presence of organics. If you need a short summary you can read this article on The Guardian but Emily should provide a complete account shortly.

I would like to spend a few words here to let my readers know what is at stake here. On 1975, NASA launched the Viking probes on Mars. One of the aims of this mission was to perform some experiments that should give evidence of life on Mars. A pair of these experiments turned out  to give favorable results giving such an evidence but the probes failed at finding any organic molecules and so these results were interpreted as due to some other chemical process at work. Indeed, the question is open yet. Should Curiosity find any evidence of organic molecular, the original findings of Viking probes would be vindicated but, more important, one should have a first evidence of life, even if bacterial, on another planet. This is for historical book indeed!

## A first paper on square root of a Brownian motion and quantum mechanics gets published!

20/11/2012

Following my series of posts on the link between the square root of a stochastic process and quantum mechanics (see here, here, here, here, here), that I proved to exist both theoretically and experimentally, I am pleased to let you know that the first paper of my collaboration with Alfonso Farina and Matteo Sedehi was finally accepted in Signal, Image and Video Processing. This paper contains the proof of what I named the “Farina-Frasca-Sedehi proposition” in my paper that claims that for a well localized free particle there exists a map between the wave function and the square root of binomial coefficients. This finally links the Pascal-Tartaglia triangle, given through binomial coefficients, to quantum mechanics and closes a question originally open by Farina and collaborators on the same journal (see here). My theorem about the square root of a stochastic process also appears in this article but without a proof.

Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v2

Farina, A., Giompapa, S., Graziano, A., Liburdi, A., Ravanelli, M., & Zirilli, F. (2011). Tartaglia-Pascal’s triangle: a historical perspective with applications Signal, Image and Video Processing DOI: 10.1007/s11760-011-0228-6