Gerald Gabrielse

Last updated
Gerald Gabrielse
NationalityAmerican
Alma mater Calvin College (B.S.)
University of Chicago (Ph.D.)
Known for antimatter, precision measurement
Awards Davisson–Germer Prize (2002)
George Ledlie Prize (2004)
Inducted into the National Academy of Sciences (2007)
Julius Edgar Lilienfeld Prize (2011)
Trotter Prize (2014)
Norman F. Ramsey Prize (2024)
Scientific career
Fields Physics
Institutions University of Washington
Harvard University
Northwestern University
Doctoral advisor Henry Gordon Berry
Other academic advisors Hans Dehmelt (postdoc)
Doctoral students Tanya Zelevinsky
Website cfp.physics.northwestern.edu/gabrielse-group/gabrielse-home.html

Gerald Gabrielse is an American physicist. He is the Board of Trustees Professor of Physics and director of the Center for Fundamental Physics at Northwestern University, and Emeritus George Vasmer Leverett Professor of Physics at Harvard University. He is primarily known for his experiments trapping and investigating antimatter, measuring the electron g-factor, [1] and measuring the electron electric dipole moment. [2] He has been described as "a leader in super-precise measurements of fundamental particles and the study of anti-matter." [3]

Contents

Career

Gabrielse attended Trinity Christian College and then Calvin College, graduating with a B.S. (honors) in 1973. He then completed his M.S. (1975) and Ph.D. (1980) in physics from the University of Chicago under Henry Gordon Berry. Gabrielse became a postdoc at the University of Washington in Seattle in 1978 under Hans Dehmelt, [4] and joined the faculty in 1985. He became professor of physics at Harvard University in 1987, and the chair of Harvard's physics department in 2000.

In 2018, Gabrielse moved to Northwestern University, becoming the director of the newly created Center for Fundamental Physics at Low Energy. [5] [6] The center is the first of its kind to be dedicated to small-scale, tabletop fundamental physics experiments. [7]

Research

Antimatter research

Gabrielse was a pioneer in the field of low energy antiproton and antihydrogen physics by proposing the trapping of antiprotons from a storage ring, cooling them in collisions with trapped electrons, [8] and the use of these to form low energy antihydrogen atoms. [9] He led the TRAP team that realized the first antiproton trapping, [10] the first electron cooling of trapped antiprotons, and the accumulation of antiprotons in a 4 Kelvin apparatus. [11] The demonstrations and methods made possible an effort that grew to involve 4 international collaborations of physicists working at CERN's Antiproton Decelerator. In 1999, Gabrielse's TRAP team made the most precise test of the Standard Model's fundamental CPT theorem by comparing the charge-to-mass ratio of a single trapped antiproton with that of a proton to a precision of 9 parts in 1011. [12] The precision of the resulting confirmation of the Standard Model prediction exceeded that of earlier comparisons by nearly a factor of 106.

Gabrielse now leads the ATRAP team at CERN, one of the two teams that first produced slow antihydrogen atoms and suspended them in a magnetic trap. [13] [14] Both TRAP and ATRAP teams used trapped antiprotons within a nested Penning trap device to produce antihydrogen atoms slow enough to be trapped in a magnetic trap. The team made the first one-particle comparison of the magnetic moments of a single proton and a single antiproton. [15] [16] Their comparison, to a precision of 5 parts per million, was 680 times more precision than previous measurements. [17]

Precision measurement

Gabrielse's group has been known to perform the most precise measurements of the electron magnetic moment by using a single trapped electron. These measurements are the most precise measurements of any single particle and are among the most stringent tests of the Standard Model. [18] Using the theory of quantum electrodynamics, a measurement of the electron magnetic moment can also be interpreted as a measurement of the fine structure constant. [19] In 2006, the group made its first measurement with an uncertainty of 0.76 parts per trillion, [20] which was 15 times more precise than a measurement that had stood for about 20 years. [21] This measurement was improved two years later by a factor of 2. [22] In 2023, the team improved upon the 2008 uncertainty by another factor of 2. [1]

In 2014, Gabrielse, as part of the ACME collaboration with John Doyle at Harvard and David DeMille at Yale, measured the electron electric dipole moment to over an order of magnitude over the previous measurement using a beam of thorium monoxide, [23] a result which had implications for the viability of supersymmetry. [24] In 2018, the ACME collaboration improved upon this upper limit by another order of magnitude. [25]

Other research contributions

Gabrielse was also one of the discoverers of the Brown-Gabrielse invariance theorem, [26] relating the free space cyclotron frequency to the measureable eigenfrequencies of an imperfect Penning trap. The theorem's applications include precise measurements of magnetic moments and precise mass spectrometry. [27] It also makes sideband mass spectrometry possible, a standard tool of nuclear physics. [28]

Gabrielse has also invented a self-shielding superconducting solenoid that uses flux conservation and a carefully chosen geometry of coupled coils to cancel strong field fluctuations due to external sources. The device was responsible for the success of the precise comparison of antiproton and proton, and also enables magnetic resonance imaging (MRI) systems to locate changing magnetic fields from external sources, such as elevators. [29]

Religious views

Gabrielse identifies himself as a scientist who is Reformed Christian. In an interview, he said:

I do not believe that science and the Bible are in conflict. However, it is possible to misunderstand the Bible and to misunderstand science. It is important to figure out what of each might be misunderstood. [30]

He has also delivered lectures on the relation between science and religion. In 2006 Gabrielse delivered a lecture titled "God of Antimatter" in the Faraday Institute for Science and Religion in Emmanuel College, Cambridge, discussing his research into antimatter as well as his personal experience with Christianity. [31] He was awarded the Trotter Prize in 2013. [32]

Trivia

Awards

Related Research Articles

<span class="mw-page-title-main">Antimatter</span> Material composed of antiparticles of the corresponding particles of ordinary matter

In modern physics, antimatter is defined as matter composed of the antiparticles of the corresponding particles in "ordinary" matter, and can be thought of as matter with reversed charge, parity, and time, known as CPT reversal. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioactive decay, but only a tiny fraction of these have successfully been bound together in experiments to form antiatoms. Minuscule numbers of antiparticles can be generated at particle accelerators; however, total artificial production has been only a few nanograms. No macroscopic amount of antimatter has ever been assembled due to the extreme cost and difficulty of production and handling. Nonetheless, antimatter is an essential component of widely-available applications related to beta decay, such as positron emission tomography, radiation therapy, and industrial imaging.

<span class="mw-page-title-main">Positron</span> Subatomic particle

The positron or antielectron is the particle with an electric charge of +1e, a spin of 1/2, and the same mass as an electron. It is the antiparticle of the electron. When a positron collides with an electron, annihilation occurs. If this collision occurs at low energies, it results in the production of two or more photons.

<span class="mw-page-title-main">Antihydrogen</span> Exotic particle made of an antiproton and positron

Antihydrogen is the antimatter counterpart of hydrogen. Whereas the common hydrogen atom is composed of an electron and proton, the antihydrogen atom is made up of a positron and antiproton. Scientists hope that studying antihydrogen may shed light on the question of why there is more matter than antimatter in the observable universe, known as the baryon asymmetry problem. Antihydrogen is produced artificially in particle accelerators.

<span class="mw-page-title-main">Antiproton</span> Subatomic particle

The antiproton,
p
, is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived, since any collision with a proton will cause both particles to be annihilated in a burst of energy.

<span class="mw-page-title-main">Samuel C. C. Ting</span> Nobel prize winning physicist

Samuel Chao Chung Ting is an American physicist who, with Burton Richter, received the Nobel Prize in 1976 for discovering the subatomic J/ψ particle.

ATHENA, also known as the AD-1 experiment, was an antimatter research project at the Antiproton Decelerator at CERN, Geneva. In August 2002, it was the first experiment to produce 50,000 low-energy antihydrogen atoms, as reported in Nature. In 2005, ATHENA was disbanded and many of the former members of the research team worked on the subsequent ALPHA experiment and AEgIS experiment.

The Antihydrogen Trap (ATRAP) collaboration at the Antiproton Decelerator facility at CERN, Geneva, is responsible for the AD-2 experiment. It is a continuation of the TRAP collaboration, which started taking data for the TRAP experiment in 1985. The TRAP experiment pioneered cold antiprotons, cold positrons, and first made the ingredients of cold antihydrogen to interact. Later ATRAP members pioneered accurate hydrogen spectroscopy and observed the first hot antihydrogen atoms.

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. The magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.

<span class="mw-page-title-main">Gravitational interaction of antimatter</span> Theory of gravity on antimatter

The gravitational interaction of antimatter with matter or antimatter has been observed by physicists. As was the consensus among physicists previously, it was experimentally confirmed that gravity attracts both matter and antimatter at the same rate within experimental error.

<span class="mw-page-title-main">PS210 experiment</span> Scientific experiment

The PS210 experiment was the first experiment that led to the observation of antihydrogen atoms produced at the Low Energy Antiproton Ring (LEAR) at CERN in 1995. The antihydrogen atoms were produced in flight and moved at nearly the speed of light. They made unique electrical signals in detectors that destroyed them almost immediately after they formed by matter–antimatter annihilation.

<span class="mw-page-title-main">Antiproton Decelerator</span> Particle storage ring at CERN, Switzerland

The Antiproton Decelerator (AD) is a storage ring at the CERN laboratory near Geneva. It was built from the Antiproton Collector (AC) to be a successor to the Low Energy Antiproton Ring (LEAR) and started operation in the year 2000. Antiprotons are created by impinging a proton beam from the Proton Synchrotron on a metal target. The AD decelerates the resultant antiprotons to an energy of 5.3 MeV, which are then ejected to one of several connected experiments.

High-precision experiments could reveal small previously unseen differences between the behavior of matter and antimatter. This prospect is appealing to physicists because it may show that nature is not Lorentz symmetric.

<span class="mw-page-title-main">Kam-Biu Luk</span>

Kam-Biu Luk is a professor of physics, with a focus on particle physics, at UC Berkeley and a senior faculty scientist in the Lawrence Berkeley National Laboratory's physics division. Luk has conducted research on neutrino oscillation and CP violation. Luk and his collaborator Yifang Wang were awarded the 2014 Panofsky Prize “for their leadership of the Daya Bay experiment, which produced the first definitive measurement of θ13 angle of the neutrino mixing matrix.” His work on neutrino oscillation also received 2016 Breakthrough Prize in Fundamental Physics shared with other teams. He also received a Doctor of Science honoris causa from the Hong Kong University of Science and Technology in 2016. Luk is a fellow of the American Physical Society, and the American Academy of Arts and Sciences.

Recycling antimatter pertains to recycling antiprotons and antihydrogen atoms.

<span class="mw-page-title-main">ALPHA experiment</span> Antimatter gravitation experiment

The Antihydrogen Laser Physics Apparatus (ALPHA), also known as AD-5, is an experiment at CERN's Antiproton Decelerator, designed to trap antihydrogen in a magnetic trap in order to study its atomic spectra. The ultimate goal of the experiment is to test CPT symmetry through comparing the respective spectra of hydrogen and antihydrogen. Scientists taking part in ALPHA include former members of the ATHENA experiment (AD-1), the first to produce cold antihydrogen in 2002.

<span class="mw-page-title-main">BASE experiment</span> Multinational collaboration

BASE, AD-8, is a multinational collaboration at the Antiproton Decelerator facility at CERN, Geneva. The goal of the Japanese and German BASE collaboration are high-precision investigations of the fundamental properties of the antiproton, namely the charge-to-mass ratio and the magnetic moment.

The rotating wall technique is a method used to compress a single-component plasma confined in an electromagnetic trap. It is one of many scientific and technological applications that rely on storing charged particles in vacuum. This technique has found extensive use in improving the quality of these traps and in tailoring of both positron and antiproton plasmas for a variety of end uses.

<span class="mw-page-title-main">John H. Malmberg</span> American physicist

John Holmes Malmberg was an American plasma physicist and a professor at the University of California, San Diego. He was known for making the first experimental measurements of Landau damping of plasma waves in 1964, as well as for his research on non-neutral plasmas and the development of the Penning–Malmberg trap.

<span class="mw-page-title-main">Penning–Malmberg trap</span> Electromagnetic device used to confine particles of a single sign of charge

The Penning–Malmberg trap, named after Frans Penning and John Malmberg, is an electromagnetic device used to confine large numbers of charged particles of a single sign of charge. Much interest in Penning–Malmberg (PM) traps arises from the fact that if the density of particles is large and the temperature is low, the gas will become a single-component plasma. While confinement of electrically neutral plasmas is generally difficult, single-species plasmas can be confined for long times in PM traps. They are the method of choice to study a variety of plasma phenomena. They are also widely used to confine antiparticles such as positrons and antiprotons for use in studies of the properties of antimatter and interactions of antiparticles with matter.

<span class="mw-page-title-main">TRAP experiment</span>

The TRAP experiment, also known as PS196, operated at the Proton Synchrotron facility of the Low Energy Antiproton Ring (LEAR) at CERN, Geneva, from 1985 to 1996. Its main goal was to compare the mass of an antiproton and a proton by trapping these particles in the penning traps. The TRAP collaboration also measured and compared the charge-to-mass ratios of antiproton and proton. Although the data-taking period ended in 1996, the analysis of datasets continued until 2006.

References

  1. 1 2 Fan, X.; Myers, T. G.; Sukra, B. A. D.; Gabrielse, G. (2023-02-13). "Measurement of the Electron Magnetic Moment". Physical Review Letters. 130 (7): 071801. arXiv: 2209.13084 . doi:10.1103/PhysRevLett.130.071801. PMID   36867820. S2CID   123962197.
  2. ↑ The ACME Collaboration; Baron, J.; Campbell, W. C.; DeMille, D.; Doyle, J. M.; Gabrielse, G.; Gurevich, Y. V.; Hess, P. W.; Hutzler, N. R. (2014-01-17). "Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron". Science. 343 (6168): 269–272. arXiv: 1310.7534 . Bibcode:2014Sci...343..269B. doi:10.1126/science.1248213. ISSN   0036-8075. PMID   24356114. S2CID   564518.
  3. ↑ "Renowned Physicist Gerald Gabrielse To Join Northwestern: Northwestern University News". www.northwestern.edu. Retrieved 2015-11-20.
  4. ↑ "Hans G. Dehmelt - Biographical". www.nobelprize.org. Retrieved 2015-11-14.
  5. ↑ "Renowned Physicist Gerald Gabrielse To Join Northwestern: Northwestern University News". www.northwestern.edu. Retrieved 2015-11-19.
  6. ↑ "Meet Physicist Jerry Gabrielse: Weinberg College - Northwestern University". www.weinberg.northwestern.edu. Retrieved 2018-07-30.
  7. ↑ Popkin, Gabriel (2018-01-10). "Step aside CERN: There's a cheaper way to break open physics". Nature. 553 (7687): 142–144. doi: 10.1038/d41586-018-00106-5 .
  8. ↑ Gabrielse, G.; Fei, X.; Orozco, L. A.; Tjoelker, R. L.; Haas, J.; Kalinowsky, H.; Trainor, T. A.; Kells, W. (1989-09-25). "Cooling and slowing of trapped antiprotons below 100 meV". Physical Review Letters. 63 (13): 1360–1363. Bibcode:1989PhRvL..63.1360G. doi:10.1103/PhysRevLett.63.1360. PMID   10040547.
  9. ↑ Gabrielse, G. "Erice Proposal" (PDF).
  10. ↑ Gabrielse, G.; Fei, X.; Helmerson, K.; Rolston, S. L.; Tjoelker, R.; Trainor, T. A.; Kalinowsky, H.; Haas, J.; Kells, W. (1986-11-17). "First Capture of Antiprotons in a Penning Trap: A Kiloelectronvolt Source". Physical Review Letters. 57 (20): 2504–2507. Bibcode:1986PhRvL..57.2504G. doi:10.1103/PhysRevLett.57.2504. PMID   10033784.
  11. ↑ Gabrielse, G. (December 1992). "Extremely Cold Antiprotons". Scientific American. 267 (6): 78. doi:10.1038/scientificamerican1292-78.
  12. ↑ Gabrielse, G.; Khabbaz, A.; Hall, D. S.; Heimann, C.; Kalinowsky, H.; Jhe, W. (1999-04-19). "Precision Mass Spectroscopy of the Antiproton and Proton Using Simultaneously Trapped Particles". Physical Review Letters. 82 (16): 3198–3201. Bibcode:1999PhRvL..82.3198G. doi:10.1103/PhysRevLett.82.3198.
  13. ↑ Gabrielse, G.; Bowden, N. S.; Oxley, P.; Speck, A.; Storry, C. H.; Tan, J. N.; Wessels, M.; Grzonka, D. (2002-10-31). "Background-Free Observation of Cold Antihydrogen with Field-Ionization Analysis of Its States" (PDF). Physical Review Letters. 89 (21): 213401. Bibcode:2002PhRvL..89u3401G. doi:10.1103/PhysRevLett.89.213401. PMID   12443407.
  14. ↑ Gabrielse, G.; Kalra, R.; Kolthammer, W. S.; McConnell, R.; Richerme, P.; Grzonka, D.; Oelert, W.; Sefzick, T. (2012-03-16). "Trapped Antihydrogen in Its Ground State". Physical Review Letters. 108 (11): 113002. arXiv: 1201.2717 . Bibcode:2012PhRvL.108k3002G. doi:10.1103/PhysRevLett.108.113002. PMID   22540471. S2CID   1480649.
  15. ↑ DiSciacca, J.; Gabrielse, G. (2012-04-10). "Direct Measurement of the Proton Magnetic Moment". Physical Review Letters. 108 (15): 153001. arXiv: 1201.3038 . Bibcode:2012PhRvL.108o3001D. doi:10.1103/PhysRevLett.108.153001. PMID   22587247. S2CID   18621981.
  16. ↑ DiSciacca, J.; Marshall, M.; Marable, K.; Gabrielse, G.; Ettenauer, S.; Tardiff, E.; Kalra, R.; Fitzakerley, D. W. (2013-03-25). "One-Particle Measurement of the Antiproton Magnetic Moment". Physical Review Letters. 110 (13): 130801. arXiv: 1301.6310 . Bibcode:2013PhRvL.110m0801D. doi:10.1103/PhysRevLett.110.130801. PMID   23581304. S2CID   14943420.
  17. ↑ "Physicists Measure Magnetic Moment of Single Antimatter Particle | Physics | Sci-News.com". www.sci-news.com. Retrieved 2015-11-20.
  18. ↑ Wilkins, Alex. "Physicists made the most precise measurement ever of a single particle". New Scientist. Retrieved 2023-03-16.
  19. ↑ Gabrielse, G.; Hanneke, D.; Kinoshita, T.; Nio, M.; Odom, B. (2006-07-17). "New Determination of the Fine Structure Constant from the Electron $g$ Value and QED". Physical Review Letters. 97 (3): 030802. doi:10.1103/PhysRevLett.97.030802. PMID   16907491. S2CID   763602.
  20. ↑ Odom, B.; Hanneke, D.; D’Urso, B.; Gabrielse, G. (2006-07-17). "New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron". Physical Review Letters. 97 (3): 030801. Bibcode:2006PhRvL..97c0801O. doi:10.1103/PhysRevLett.97.030801. PMID   16907490.
  21. ↑ Schwarzschild, Bertram (2006-08-01). "Gyromagnetic ratio of a lone trapped electron is measured to better than a part per trillion". Physics Today. 59 (8): 15–17. Bibcode:2006PhT....59h..15S. doi:10.1063/1.2349714. ISSN   0031-9228.
  22. ↑ Hanneke, D.; Fogwell, S.; Gabrielse, G. (2008-03-26). "New Measurement of the Electron Magnetic Moment and the Fine Structure Constant". Physical Review Letters. 100 (12): 120801. arXiv: 0801.1134 . Bibcode:2008PhRvL.100l0801H. doi:10.1103/PhysRevLett.100.120801. PMID   18517850. S2CID   2216271.
  23. ↑ Collaboration, The ACME; Baron, J.; Campbell, W. C.; DeMille, D.; Doyle, J. M.; Gabrielse, G.; Gurevich, Y. V.; Hess, P. W.; Hutzler, N. R. (2014-01-17). "Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron". Science. 343 (6168): 269–272. arXiv: 1310.7534 . Bibcode:2014Sci...343..269B. doi:10.1126/science.1248213. ISSN   0036-8075. PMID   24356114. S2CID   564518.
  24. ↑ "'Perfect' Electron Roundness Bruises Supersymmetry : DNews". DNews. Retrieved 2015-11-14.
  25. ↑ Andreev, V.; Ang, D. G.; DeMille, D.; Doyle, J. M.; Gabrielse, G.; Haefner, J.; Hutzler, N. R.; Lasner, Z.; Meisenhelder, C.; O’Leary, B. R.; Panda, C. D.; West, A. D.; West, E. P.; Wu, X.; ACME Collaboration (2018-10-17). "Improved limit on the electric dipole moment of the electron". Nature . 562 (7727): 355–360. doi:10.1038/s41586-018-0599-8. ISSN   1476-4687. PMID   30333583. S2CID   186242690.
  26. ↑ Brown, Lowell S.; Gabrielse, Gerald (1982-04-01). "Precision spectroscopy of a charged particle in an imperfect Penning trap". Physical Review A. 25 (4): 2423–2425. Bibcode:1982PhRvA..25.2423B. doi:10.1103/PhysRevA.25.2423.
  27. ↑ Gabrielse, G. (2009-01-15). "The true cyclotron frequency for particles and ions in a Penning trap". International Journal of Mass Spectrometry. 279 (2–3): 107–112. Bibcode:2009IJMSp.279..107G. doi:10.1016/j.ijms.2008.10.015.
  28. ↑ Gabrielse, G. (2009-04-27). "Why Is Sideband Mass Spectrometry Possible with Ions in a Penning Trap?". Physical Review Letters. 102 (17): 172501. Bibcode:2009PhRvL.102q2501G. doi:10.1103/PhysRevLett.102.172501. PMID   19518777. S2CID   32016734.
  29. ↑ Gabrielse, G.; Tan, J. (1988-05-15). "Self-shielding superconducting solenoid systems". Journal of Applied Physics. 63 (10): 5143–5148. Bibcode:1988JAP....63.5143G. doi:10.1063/1.340416. ISSN   0021-8979.
  30. 1 2 "Distinguished Alumni Award: Gerald Gabrielse '73". www.calvin.edu. Archived from the original on 2016-03-03. Retrieved 2015-11-14.
  31. ↑ "Discussion: God of Antimatter - Gerald Gabrielse". www.faraday.st-edmunds.cam.ac.uk. Archived from the original on 2016-03-04. Retrieved 2015-11-14.
  32. 1 2 "Trotter Lecture Series". www.science.tamu.edu. Archived from the original on 2023-05-06. Retrieved 2015-11-14.
  33. ↑ L.J. Lapidus, D. Enzer and G. Gabrielse (1999-08-02). "Stochastic Phase-Switching of a Parametrically-Driven Electron in a Penning Trap" (PDF). Physical Review Letters, vol. 83 no. 5, 899.
  34. ↑ "APS: Prime-time physics : In The Field". blogs.nature.com. Retrieved 2015-11-14.
  35. ↑ Hsu, Jeremy (2009-05-13). "The Truth about Angels, Demons and Antimatter". livescience.com. Retrieved 2023-11-01.
  36. ↑ "APS Fellow Archive". www.aps.org. Retrieved 2023-11-01.
  37. ↑ "Past Alumni Of The Year (Technical)". Trinity Christian College. Retrieved 2023-11-01.
  38. ↑ "Prize Recipient". www.aps.org. Retrieved 2015-11-14.
  39. ↑ Office, Ken Gewertz Harvard News (2004-04-22). "George Ledlie Prize goes to physicist Gerald Gabrielse". Harvard Gazette. Retrieved 2023-11-01.
  40. ↑ "Gerald Gabrielse". www.nasonline.org. Retrieved 2015-11-14.
  41. ↑ "Zachariasen Memorial Lectures | Department of Physics | The University of Chicago". physics.uchicago.edu. Retrieved 2023-11-01.
  42. ↑ Gabrielse, Gerald (2009), Duplantier, Bertrand; Raimond, Jean-Michel; Rivasseau, Vincent (eds.), "Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant", The Spin: Poincaré Seminar 2007, Progress in Mathematical Physics, Basel: Birkhäuser, pp. 105–145, doi:10.1007/978-3-7643-8799-0_4, ISBN   978-3-7643-8799-0 , retrieved 2023-11-09
  43. ↑ "Séminaire Bourbaphy". www.bourbaphy.fr. Retrieved 2023-11-09.
  44. ↑ "Tomassoni Chisesi Prize | Dipartimento di Fisica". www.phys.uniroma1.it. Retrieved 2023-11-01.
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