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Register a new userFrom Ramanujan to renormalization: the art of doing away with divergences and arriving at physical results
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Added by
Wolfgang Bietenholz
Publication date
2021
fields
Physics
and research's language is
English
Authors
Wolfgang Bietenholz
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A century ago, Srinivasa Ramanujan -- the great self-taught Indian genius of mathematics -- died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding results to different branches of mathematics, like analysis and number theory, with a focus on special functions and series. Here we refer to apparently weird values which he assigned to two simple divergent series, $sum_{n geq 1} n$ and $sum_{n geq 1} n^{3}$. These values are sensible, however, as analytic continuations, which correspond to Riemanns $zeta$-function. Moreover, they have applications in physics: we discuss the vacuum energy of the photon field, from which one can derive the Casimir force, which has been experimentally measured. We further discuss its interpretation, which remains controversial. This is a simple way to illustrate the concept of renormalization, which is vital in quantum field theory.
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Dedicated to the centenary of the Ioffe Institute, the article contains the shortest review of scientific achievements of the theorists of the institute during this time. We concentrate mainly on research in the field of elementary particle physics, astrophysics, nuclear theory and atoms. To obtain very important scientific results became possible because outstanding theoreticians worked at this Institute. The high level of research persisted in spite of several mass moves of theorists - then to Kharkov, then to Moscow, then abroad. The author can testify to the atmosphere that reigned in the FTI in person, since he works at this institute since 1958. The article deals not only with research activity, but also with the famous physics schools and their outstanding cultural programs. We present also examples of extraordinary successful activity of theorists far beyond the field of their narrow specialization.
We survey early Indian ideas on the speed of light and the size of the universe. A context is provided for Sayanas statement (14th century)that the speed is 2,202 yojanas per half nimesha (186,000 miles per second!). It is shown how this statement may have emerged from early Puranic notions regarding the size of the universe. Although this value can only be considered to be an amazing coincidence, the Puranic cosmology at the basis of this assertion illuminates many ancient ideas of space and time.
Indigenous peoples across the world observe the motions and positions of stars to develop seasonal calendars. Additionally, changing properties of stars, such as their brightness and colour, are also used for predicting weather. Combining archival studies with ethnographic fieldwork in Australias Torres Strait, we explore the various ways Indigenous peoples utilise stellar scintillation (twinkling) as an indicator for predicting weather and seasonal change, discussing the scientific underpinnings of this knowledge. By observing subtle changes in the ways the stars twinkle, Meriam people gauge changing trade winds, approaching wet weather, and temperature changes. We then explore how the Northern Dene of Arctic North America utilise stellar scintillation to forecast weather.
Twisted, or vortex, particles refer to freely propagating non-plane-wave states with helicoidal wave fronts. In this state, the particle possesses a non-zero orbital angular momentum with respect to its average propagation direction. Twisted photons and electrons have been experimentally demonstrated, and creation of other particles in twisted states can be anticipated. If brought in collisions, twisted states offer a new degree of freedom to particle physics, and it is timely to analyze what new insights may follow. Here, we theoretically investigate resonance production in twisted photon collisions and twisted $e^+e^-$ annihilation and show that these processes emerge as a completely novel probe of spin and parity-sensitive observables in fully inclusive cross sections with unpolarized initial particles. This is possible because the initial state with a non-zero angular momentum explicitly breaks the left-right symmetry even when averaging over helicities. In particular, we show how one can produce almost $100%$ polarized vector mesons in unpolarized twisted $e^+e^-$ annihilation and how to control its polarization state.
Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs have found numerous applications in combinatorics and computer science. In recent years, a high dimensional theory has emerged. In this paper these developments are surveyed. After explaining their connection to the Ramanujan conjecture we will present some old and new results with an emphasis on random walks on these discrete objects and on the Euclidean spheres. The latter lead to golden gates which are of importance in quantum computation.
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