#paperoftheday — Public Fediverse posts

#paperOfTheDay "Über die Eigenkräfte der Elementarteilchen I" from 1933.
This is another paper from the very early days of #quantumFieldTheory , concerned with the question of the seemingly infinite self-energy of the electron in its own electromagnetic field, namely: If the electron is point-like, then its classical electromagnetic field should be infinite at its location, which is clearly nonsense.
The present paper presents a more refined relativistic analysis, starting from the assumption that the locations where the electron "generates" the field and where it "feels" it are distinct by a small vector r. If r is space like (i.e. the two locations differ by a distance that is farther than the distance that light could travel in the same time interval), one recovers the familiar divergence. On the other hand, if r is inside the light cone (i.e. the electron "feels" its own field in its causal future or past), the divergence is absent even in the limit r->0. However, this computation only works for a classical electron in a classical electromagnetic field. Using the Dirac equation for the electron, new obstacles appear.
The present article is typical for the time when #quantum theory was being developed, but it was not at all clear how to interpret it, or whether it was even correct. Schrödinger coined the term "Zitterbewegung" for the intuition of the electron making infinitely fine random jumps at light speed; the present paper mentions this Zitterbewegung as an obvious reason for difficulties in the self-energy. Today, I would say that Zitterbewegung can be an intuitive picture, but the laws of classical #physics are simply not valid at so small scales.
https://link.springer.com/article/10.1007/BF01341363

The #paperOfTheDay is a classic of #thermodynamics : "Equation of state in the Neighborhood of the critical point" from 1965. Here, Benjamin Widom introduces what is now known as "Widom scaling".
Generically, the properties of a fluid might depend on parameters, such as temperature or density, through power laws. There are certain critical points in the phase space, i.e. certain temperatures, densities, etc., where the behaviour of the fluid changes qualitatively. The observation is that close to the critical point, the exponents of the various power laws have different numerical values than what one would expect classically. For example, the specific heat diverges at a power law, but the exponent of divergence is not what one would expect from the conventional equation of state.
Widom's paper now makes a specific conjecture: Near a critical point, the equation of state should be altered by introducing an arbitrary function of density of temperature, however, this function is assumed to be homogeneous. That is if x is temperature and y is density, it is a function of the form e.g. x^c * f(y/x), where f is an arbitrary function of y/x, and c is a constant. It turns out that almost all experimental observations can be described from this conjecture without knowing the functional form of f. The scaling exponent c alone is sufficient to give rise to the non-classical power laws and the relations between them.
This paper is significant because it is an early (and purely heuristic) version of universality: The behaviour of systems in #statisticalPhysics at the critical point is largely determined from structural properties, independently of concrete details.
https://pubs.aip.org/aip/jcp/article-abstract/43/11/3898/210917/Equation-of-State-in-the-Neighborhood-of-the?redirectedFrom=fulltext

The #paperOfTheDay is Wolfgang Pauli's letter to experimental physicists Lise Meitner and Hans Geiger in December 1930. Pauli explains that he is unable to join their meeting due to a ball event in Zürich, but still wants to inform them about his newest theory.
At that time, beta decay had been well confirmed experimentally, but the energies and momenta of the observed particles did not add up. This had puzzled physicists to a degree such that Debye, quoted by Pauli, said "Oh, better don't think about this at all, like about new taxes!".
Pauli now proposes that there actually is a new type of particle that has so far escaped observation, which he calls "neutron". He makes some brief comments on the mass and interaction of such a particle. He will as of now not officially publish these since it is pure speculation and there is currently no experimental evidence for this particle. Instead, he has written this letter to the experimental physicists, which ends "Also, liebe Radioaktive, prüfet und richtet!" -- "Hence, dear radioactive [ladies and gentlemen], scrutinize and judge!"
A few years later, Fermi developed a full theory for Pauli's particle, and renamed it into "neutrino". The direct experimental confirmation of the #neutrino is tricky, and would take another several years. Conversely, the nuclear constituent particle we now know as "neutron", was experimentally observed already in 1932. #physics #radioactive
German letter: https://cds.cern.ch/record/83282/files/meitner
English translation: https://radioactivity.eu.com/articles/phenomenon/paulis-letter

#PaperOfTheDay is "Full phase diagram of the massive Gross-Neveu model" from 2006.
The Gross-Neveu model is a #quantumFieldTheory of fermions in two spacetime dimensions. In the absence of a bare mass term, it has a discrete chiral symmetry (a few days ago I shared a paper where that symmetry is promoted to a continuous symmetry by adding a second interaction term). The present paper, conversely, is about the case where the mass is non-zero. Then, chiral symmetry is broken.
They consider the theory from a #thermodynamics perspective, where the variables are temperature (i.e. the Planck constant in quantum field language), chemical potential (i.e. a constant offset to energy), and the mass of the particle. Using a clever ansatz, they are able to compute the full phase diagram of the Gross-Neveu field as function of the three variables. As had long been known, if the bare mass vanishes, then the model generates a dynamic mass for the fermion at low enough temperature and chemical potential. It had previously been believed that at non-vanishing bare mass, there would be a discontinuous change in the effective mass from large to small as the temperature is increased. The central result of the present paper is that this is false: Instead, in the boundary region, there is another phase where the field is spacially non-homogeneous, it forms a periodic crystal. Below, one has a heavy fermion, above the fermion is light, and the new phase is something different altogether.
https://www.sciencedirect.com/science/article/abs/pii/S0003491605002915

The #paperOfTheDay is "Renormalons and fixed points". This article from 1996 investigates the relation between #renormalons and infrared behaviour of #QCD. A renormalon is an effect that can lead to the divergence of a perturbation series, and such effects have been observed in various contexts. What has never become quite clear (at least to me) is the precise logical relation between its different incarnations: Divergence of the series, Landau poles, the peculiarities of QCD (renormalons exist in scalar theories as well!), non-trivial fixed points, and questions of uniqueness and resummability. The present paper points out some difficulties -- namely that some of the quantities involved are only defined perturbatively, or are sensitive to choices of analytic continuation. These considerations are interesting and not trivial, but I find it sometimes hard to follow the article since it has no explicit structure such as subsections or theorems, it is simply one continuous discussion. Or maybe I've just become too much of a mathematician by now.
#dailyPaperChallenge https://www.sciencedirect.com/science/article/pii/0370269396000615

A few days ago in the #dailyPaperChallenge I read Veneziano's proposal for a 4-point amplitude. This Friday, my #paperOfTheDay was "Alternative Construction of Crossing-Symmetric Amplitudes with Regge Behaviour" from 1969, were another, more general, expression is proposed by Virasoro. Overall, the spirit is very similar to Veneziaon's article: Propose a formula and discuss its properties. In particular, the Virasoro amplitude reduces to the Veneziano one if an extra condition is imposed, and at the same time it is argued that this condition is not satisfied for some realistic scattering processes, and therefore Virasoro's amplitude should be expected to better reflect reality than Veneziano's. Again, such heuristic arguments have become somewhat obsolete by now since we now know #QCD as a fundamental theory, and don't have to guess amplitudes any more. Still, the Virasoro amplitude stays relevant for certain theoretical considerations. https://journals.aps.org/pr/abstract/10.1103/PhysRev.177.2309