# André Petermann
**André Petermann** (1922 – 2011) was a theoretical physicist, one of the first members of the CERN Theory Division, who with his advisor [Ernst Stueckelberg](https://www.edgepedia.org/ernst-stueckelberg) pioneered the renormalization group and who corrected the fourth-order quantum electrodynamic prediction for the electron's anomalous magnetic moment. He died in August 2011 in his 89th year.[1](https://home.cern/andre-petermann-1922-2011/) The renormalization-group work Petermann developed with Stueckelberg underlies modern phase-transition theory, asymptotic freedom, and unification, and Kenneth Wilson paid tribute to their paper when accepting the Nobel Prize.[1](https://home.cern/andre-petermann-1922-2011/) He is also, belatedly, credited with an independent quark model published in French in 1965, received before Gell-Mann's and Zweig's papers and unnoticed for fifty-five years.[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4)
| Key fact | Detail |
|---|---|
| Life | 1922 – August 2011; one of the first members of the CERN Theory Division[1](https://home.cern/andre-petermann-1922-2011/) |
| Career | PhD at Lausanne University 1953; junior position at Manchester University 1954–1955; senior staff at CERN 1955–1987[3](https://inspirehep.net/authors/1764976) |
| Renormalization group | With Stueckelberg, discovered in 1951 that couplings and masses "run" with the invariant four-momentum q², and in 1953 proposed the invariance group they called the "renormalization group"[4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/) |
| Electron g-2 | Corrected Karplus and Kroll's 1950 fourth-order coefficient from −2.973 to −0.328 in 1957; diagram IIc from −3.18 to −0.564[5](http://progress-in-physics.com/2020/PP-60-09.PDF) |
| Muon g-2 | Pioneering next-to-leading-order correction to the muon's anomalous magnetic moment, key to the CERN measurement and still a reference[1](https://home.cern/andre-petermann-1922-2011/) |
| Quark model | "Properties of Strangeness and a Mass Formula for Vector Mesons", received by *Nuclear Physics* on 30 December 1963, published March 1965, unnoticed for 55 years[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4) |
## Life and career
Petermann took his PhD at the University of Lausanne in 1953, spent 1954 to 1955 in a junior position at the [University of Manchester](https://www.edgepedia.org/university-of-manchester), and joined CERN as senior staff in 1955, remaining until 1987.[3](https://inspirehep.net/authors/1764976) He was among the very first CERN staff members, joining the small theory group at the [Niels Bohr Institute](https://www.edgepedia.org/niels-bohr-institute) in Copenhagen before it moved to Geneva, first to barracks at Cointrin, then to the University of Geneva, and finally to the Meyrin site.[1](https://home.cern/andre-petermann-1922-2011/) His advisor in Geneva was Ernst Stueckelberg, with whom he did the renormalization-group work.[1](https://home.cern/andre-petermann-1922-2011/) In later years his interests extended to grand unification and superstring compactifications.[1](https://home.cern/andre-petermann-1922-2011/) Colleagues describe him as a recluse, and he spelled his name "Peterman" in most of his other publications.[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4)
## The 1957 electron g-2 calculation
The [anomalous magnetic moment of the electron](https://www.edgepedia.org/anomalous-magnetic-moment-of-the-electron), usually written g-2, receives corrections from quantum electrodynamic (QED) loop diagrams. Karplus and Kroll computed the fourth-order coefficient in 1950 and obtained −2.973. Petermann corrected this seven years later to −0.328, almost ten times smaller in magnitude.[5](http://progress-in-physics.com/2020/PP-60-09.PDF) The error lay in one [Feynman diagram](https://www.edgepedia.org/feynman-diagram), labeled IIc, whose value Karplus and Kroll had given as −3.18 (in units of α²/π², with a logarithmic term) and which Petermann found to be −0.564.[5](http://progress-in-physics.com/2020/PP-60-09.PDF)
**How the error was found.** Petermann was the first to identify the mistake, using numerical bounds to show that diagram IIc fell outside rigorous limits: he first bounded it as IIc = −1.02 ± 0.53, then as −0.60 ± 0.11, in contradiction with Karplus and Kroll's −3.18.[5](http://progress-in-physics.com/2020/PP-60-09.PDF) His 1957 paper in *Helvetica Physica Acta* states the IIc term as (−0.60 ± 0.11) α²/π² − ½ (α²/π²) log(λ²/m²), against the earlier authors' −3.18 α²/π² − ½ (α²/π²) log(λ²/m²).[6](https://www.e-periodica.ch/cntmng?pid=hpa-001%3A1957%3A30%3A%3A997) His definitive analytic evaluation gave the five diagram values I = −0.467, IIa = 0.778, IIc = −0.564, IId = −0.090, IIe = 0.016, totaling −0.328, in consensus with Sommerfield's independent calculation.[5](http://progress-in-physics.com/2020/PP-60-09.PDF)
**Why it mattered.** The electron g-2, together with the [Lamb shift](https://www.edgepedia.org/lamb-shift), provided the first experimental confirmation that renormalized QED is the realistic theory of the electromagnetic interaction.[7](https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.167.62/5278932/167-62.pdf) Petermann's own paper reports the total fourth-order moment as μ(4) = (−0.39 ± 0.11)(α²/π²), notes that the new value increases the Lamb shift by (0.82 ± 0.03) Mc/s, and derives a fine-structure constant of 1/α = 137.0384.[6](https://www.e-periodica.ch/cntmng?pid=hpa-001%3A1957%3A30%3A%3A997) The modern recalculation gives the coefficient as −0.328 478 965 579..., confirming Petermann's 1957 value of −0.328.[7](https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.167.62/5278932/167-62.pdf) Modern QED now reproduces the electron g-factor to 12 decimal places: Gabrielse's 2008 experimental value is 1.001 159 652 180 73(28) against Kinoshita's 2018 theoretical value 1.001 159 652 182 032(720).[5](http://progress-in-physics.com/2020/PP-60-09.PDF)
## The muon g-2 work at CERN
Petermann also made a pioneering calculation of the next-to-leading-order correction to the anomalous magnetic moment of the muon, a particle about 200 times heavier than the electron. This was key to the interpretation of the famous CERN experimental measurement of the quantity, and it is still a reference today.[1](https://home.cern/andre-petermann-1922-2011/) By 1960 he had made the most accurate theoretical prediction of the muon's g-2, but at that time there was no high-precision measurement because technical problems remained to be solved.[4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/) The CERN experiment used a 6-m long "flat magnet", and Petermann worked nights with the experimentalists in the SC Experimental Hall.[4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/)
## The Petermann renormalization group
The first appearance of a renormalization group concept in the literature is in the Stueckelberg–Petermann papers of 1951 and 1953, though the authors used the term "groupe de normalisation", or normalization group.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) In 1951 the two discovered that quantities such as the gauge couplings and the masses must "run" with q², the invariant four-momentum of a process; in 1953 they proposed that the freedom in choosing renormalization subtraction points obeys the rules of an invariance group, which they called the "renormalization group".[4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/)
In modern terms, the Stückelberg–Petermann renormalization group is the group of finite renormalizations of the S-matrix in the framework of causal perturbation theory.[9](https://www.numdam.org/articles/10.1142/S1793744212400014) It arose from the causal perturbation theory program, while the Gell-Mann–Low group arose from debates about the consistency of QED; these are two distinct strands, or "twin origins", of 1950s physics.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) The idea of Peterman and Stueckelberg from 1953 was used by Gell-Mann and Low in 1954 to argue that a renormalizable theory could have a fixed point in the ultraviolet.[10](https://arxiv.org/html/hep-th/9808154)
## Comparison with other renormalization groups
The Stueckelberg–Petermann group is more general than the Gell-Mann–Low/Bogoliubov–Shirkov version: it spans the full space of renormalization schemes, including subtraction conventions, of which the Bogoliubov–Shirkov group is a subgroup, or, more correctly according to recent mathematical physics treatments, a cocycle.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) It is conceptually distinct from Wilson's renormalization group, which describes dependence on a ultraviolet cutoff Λ via a functional-integral formalism.[9](https://www.numdam.org/articles/10.1142/S1793744212400014) The two approaches are nonetheless related: the restriction of Wilson-type flow operators to local interactions can be approximated by a subfamily of the Stückelberg–Petermann renormalization group.[9](https://www.numdam.org/articles/10.1142/S1793744212400014) The running of couplings that Stueckelberg and Petermann discovered is described as ultimately motivating grand unification, supersymmetry, and non-point-like descriptions including relativistic quantum-string theory.[4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/)
## An independent quark model, unnoticed for 55 years
Petermann's paper "Properties of Strangeness and a Mass Formula for Vector Mesons", written in French, was received by *Nuclear Physics* on 30 December 1963 but not published until March 1965, and it went almost unnoticed for fifty-five years.[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4) The paper proposed that hadrons are composed of three constituents with non-integral charges, an independent quark model. Petermann, a recluse, did not follow it up, and it was publicised only by De Rújula in 2004 and 2014.[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4) On priority, Gell-Mann's paper in *Physics Letters* was received 4 January 1964 and Zweig's CERN preprint is dated 17 January 1964, while Petermann's paper was received 30 December 1963, earlier than both.[11](https://ar5iv.labs.arxiv.org/html/2001.04843) Its obscurity is attributed to its being in French, a title that did not reflect its contents, and to Zweig's more comprehensive work.[2](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4)
## Recognition and historical neglect
When Kenneth Wilson was awarded the Nobel Physics Prize for applying the renormalization group to critical phenomena, he acknowledged a congratulatory letter from Petermann by paying tribute to the joint paper with Stueckelberg for initiating the whole renormalization-group effort.[1](https://home.cern/andre-petermann-1922-2011/) The limited readership of the Stueckelberg–Petermann papers is partly explained by Stueckelberg's unorthodox causal formulation of perturbative QFT and their idiosyncratic notation; the papers did have an impact on later developments, though by a circuitous route.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) Their concept has been revived in mathematical physics, where the transformation group linking perturbative S-matrix developments is viewed as a fundamental result rooted in their distribution-theoretic approach to ultraviolet divergences.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf)
## Primary sources and bibliography
The foundational paper is Stueckelberg and Petermann, "La normalisation des constantes dans la théorie des quanta", *Helvetica Physica Acta* 26 (1953) 499–520.[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) The g-2 correction appeared as "Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron", *Nuclear Physics* 3 (1957) 689–690, DOI 10.1016/0029-5582(57)90007-X, also cataloged as a CERN Yellow Reports: Monographs entry, and in *Helvetica Physica Acta* 30 (1957).[12](https://inspirehep.net/literature/43838) • [6](https://www.e-periodica.ch/cntmng?pid=hpa-001%3A1957%3A30%3A%3A997) Petermann later authored "Renormalization group and the deep structure of the proton", *Physics Reports* 53(3):157–248 (1979).[8](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf) CERN's obituary and a CERN Courier memoir document his life at the laboratory.[1](https://home.cern/andre-petermann-1922-2011/) • [4](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/)
## References
1. [André Petermann (1922 – 2011), CERN](https://home.cern/andre-petermann-1922-2011/)
2. [From concrete quarks to QCD: a personal perspective, EPJ H (2023)](https://link.springer.com/article/10.1140/epjh/s13129-023-00061-4)
3. [Andreas Petermann, INSPIRE-HEP](https://inspirehep.net/authors/1764976)
4. [Interactions with André Petermann, CERN Courier](https://cern-courier.web.cern.ch/a/interactions-with-andr-petermann/)
5. [The Unpublished Feynman Diagram IIc, Progress in Physics (2020)](http://progress-in-physics.com/2020/PP-60-09.PDF)
6. [A. Petermann, Fourth order magnetic moment of the electron, Helvetica Physica Acta 30 (1957)](https://www.e-periodica.ch/cntmng?pid=hpa-001%3A1957%3A30%3A%3A997)
7. [Progress of Theoretical Physics Supplement 167, review on g-2](https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.167.62/5278932/167-62.pdf)
8. [The Twin Origins of the Renormalization Group (preprint)](https://philsci-archive.pitt.edu/21690/1/Twin%20Origins%20of%20the%20Renormalization%20Group%20Preprint%20Version.pdf)
9. [Connection between the renormalization groups of Stückelberg–Petermann and Wilson](https://www.numdam.org/articles/10.1142/S1793744212400014)
10. [arXiv hep-th/9808154](https://arxiv.org/html/hep-th/9808154)
11. [The idea of quarks: towards restoring of historical justice (arXiv)](https://ar5iv.labs.arxiv.org/html/2001.04843)
12. [Fourth-Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron, INSPIRE-HEP record](https://inspirehep.net/literature/43838)
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*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Physicists and astronomers › Researchers in particle, nuclear, and high-energy theoretical physics › Quantum field theory and mathematical physics*
*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026*
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