Lautaro Vergara-Cofré
@vergaralautaro.bsky.social
Chilean physicist.
Posting mainly about history of physics.
Too many interesting things to learn, too few time.
Born at 316.91 ppm
Posting mainly about history of physics.
Too many interesting things to learn, too few time.
Born at 316.91 ppm
cementing his reputation as the "invisible man" of the rotation group, a man whose pivotal mathematical contributions and ardent social reform efforts remain under-recognized.
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October 6, 2025 at 5:35 PM
cementing his reputation as the "invisible man" of the rotation group, a man whose pivotal mathematical contributions and ardent social reform efforts remain under-recognized.
8/8
8/8
displacements, doing more on the subject than anyone for decades.
Rodrigues died in relative obscurity, with even the precise date of his death being uncertain. The fact that he was a mathematician was often forgotten by early historians of Saint-Simonism,
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Rodrigues died in relative obscurity, with even the precise date of his death being uncertain. The fact that he was a mathematician was often forgotten by early historians of Saint-Simonism,
7/
October 6, 2025 at 5:35 PM
displacements, doing more on the subject than anyone for decades.
Rodrigues died in relative obscurity, with even the precise date of his death being uncertain. The fact that he was a mathematician was often forgotten by early historians of Saint-Simonism,
7/
Rodrigues died in relative obscurity, with even the precise date of his death being uncertain. The fact that he was a mathematician was often forgotten by early historians of Saint-Simonism,
7/
more extreme factions.
After a long period away from mathematics, Rodrigues published his most significant mathematical work in 1840 on the rotation group. This paper broke from the traditional dynamics-focused approach of Euler to study the geometry of rigid body
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After a long period away from mathematics, Rodrigues published his most significant mathematical work in 1840 on the rotation group. This paper broke from the traditional dynamics-focused approach of Euler to study the geometry of rigid body
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October 6, 2025 at 5:35 PM
more extreme factions.
After a long period away from mathematics, Rodrigues published his most significant mathematical work in 1840 on the rotation group. This paper broke from the traditional dynamics-focused approach of Euler to study the geometry of rigid body
6/
After a long period away from mathematics, Rodrigues published his most significant mathematical work in 1840 on the rotation group. This paper broke from the traditional dynamics-focused approach of Euler to study the geometry of rigid body
6/
helped lead the movement, championing the rights of women and workers, and publishing extensively on social issues, banking reform, and the development of French railways. His ardent Saint-Simonism, however, led to legal trouble and ultimately a split from the movement's
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October 6, 2025 at 5:34 PM
helped lead the movement, championing the rights of women and workers, and publishing extensively on social issues, banking reform, and the development of French railways. His ardent Saint-Simonism, however, led to legal trouble and ultimately a split from the movement's
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though his identity is largely unknown.
Shifting from academia, Rodrigues followed his family into finance but soon became a devoted disciple and financial supporter of the charismatic utopian socialist Claude-Henri de Saint-Simon. Following Saint-Simon's death, Rodrigues
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Shifting from academia, Rodrigues followed his family into finance but soon became a devoted disciple and financial supporter of the charismatic utopian socialist Claude-Henri de Saint-Simon. Following Saint-Simon's death, Rodrigues
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October 6, 2025 at 5:34 PM
though his identity is largely unknown.
Shifting from academia, Rodrigues followed his family into finance but soon became a devoted disciple and financial supporter of the charismatic utopian socialist Claude-Henri de Saint-Simon. Following Saint-Simon's death, Rodrigues
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Shifting from academia, Rodrigues followed his family into finance but soon became a devoted disciple and financial supporter of the charismatic utopian socialist Claude-Henri de Saint-Simon. Following Saint-Simon's death, Rodrigues
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to an academic career despite his talent. He earned his Docteur ès sciences from the University of Paris in 1815, and his thesis contained the famous Rodrigues formula for Legendre polynomials:
This formula is his main legacy in modern physics
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This formula is his main legacy in modern physics
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October 6, 2025 at 5:33 PM
to an academic career despite his talent. He earned his Docteur ès sciences from the University of Paris in 1815, and his thesis contained the famous Rodrigues formula for Legendre polynomials:
This formula is his main legacy in modern physics
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This formula is his main legacy in modern physics
3/
Born a year after the foundation of the École Polytechnique, Rodrigues lived in a period of intense mathematical development and utopian socialist fervor.
As a Jew, he gained citizenship rights under Napoleon, but the Bourbon restoration in 1815 blocked his path
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As a Jew, he gained citizenship rights under Napoleon, but the Bourbon restoration in 1815 blocked his path
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October 6, 2025 at 5:33 PM
Born a year after the foundation of the École Polytechnique, Rodrigues lived in a period of intense mathematical development and utopian socialist fervor.
As a Jew, he gained citizenship rights under Napoleon, but the Bourbon restoration in 1815 blocked his path
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As a Jew, he gained citizenship rights under Napoleon, but the Bourbon restoration in 1815 blocked his path
2/
N.B.: Sorry. In 8/, it should say:
The formula, based on an assumption that the mass operator is a sum of a dominant SU(3)-invariant term and a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet...
The formula, based on an assumption that the mass operator is a sum of a dominant SU(3)-invariant term and a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet...
August 25, 2025 at 3:33 PM
N.B.: Sorry. In 8/, it should say:
The formula, based on an assumption that the mass operator is a sum of a dominant SU(3)-invariant term and a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet...
The formula, based on an assumption that the mass operator is a sum of a dominant SU(3)-invariant term and a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet...
Indeed :)
Thanks.
Thanks.
August 25, 2025 at 3:16 PM
Indeed :)
Thanks.
Thanks.
to propose the existence of more fundamental, subatomic particles: the quarks.
--end
--end
August 25, 2025 at 1:24 PM
to propose the existence of more fundamental, subatomic particles: the quarks.
--end
--end
The success of the mass formula, combined with the fact that the Eightfold Way used an abstract mathematical representation that was not the most fundamental one, led Gell-Mann and, independently, George Zweig and André Petermann
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August 25, 2025 at 1:24 PM
The success of the mass formula, combined with the fact that the Eightfold Way used an abstract mathematical representation that was not the most fundamental one, led Gell-Mann and, independently, George Zweig and André Petermann
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that depend on the principal quantum numbers of the SU(3) representation but not on I, I₃, or Y.
The Gell-Mann-Okubo mass formula was part of Gell-Mann's earlier classification scheme known as the Eightfold Way (or SU(3) flavor symmetry).
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The Gell-Mann-Okubo mass formula was part of Gell-Mann's earlier classification scheme known as the Eightfold Way (or SU(3) flavor symmetry).
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August 25, 2025 at 1:23 PM
that depend on the principal quantum numbers of the SU(3) representation but not on I, I₃, or Y.
The Gell-Mann-Okubo mass formula was part of Gell-Mann's earlier classification scheme known as the Eightfold Way (or SU(3) flavor symmetry).
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The Gell-Mann-Okubo mass formula was part of Gell-Mann's earlier classification scheme known as the Eightfold Way (or SU(3) flavor symmetry).
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This relation was confirmed with the discovery of the omega-minus particle in 1964, a key triumph for SU(3) theory.
The Gell-Mann-Okubo formula:
M(I,Y)=a+bY+c[(1/4)Y²−I(I+1)]
where M is the mass, Y is the hypercharge, I is the isospin, and a, b, and c are constants
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The Gell-Mann-Okubo formula:
M(I,Y)=a+bY+c[(1/4)Y²−I(I+1)]
where M is the mass, Y is the hypercharge, I is the isospin, and a, b, and c are constants
9/
August 25, 2025 at 1:22 PM
This relation was confirmed with the discovery of the omega-minus particle in 1964, a key triumph for SU(3) theory.
The Gell-Mann-Okubo formula:
M(I,Y)=a+bY+c[(1/4)Y²−I(I+1)]
where M is the mass, Y is the hypercharge, I is the isospin, and a, b, and c are constants
9/
The Gell-Mann-Okubo formula:
M(I,Y)=a+bY+c[(1/4)Y²−I(I+1)]
where M is the mass, Y is the hypercharge, I is the isospin, and a, b, and c are constants
9/
a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet.
For the baryon octet, the formula yielded a mass relation that was well-satisfied by existing data. For the baryon decouplet, it predicted an equal mass spacing between members.
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For the baryon octet, the formula yielded a mass relation that was well-satisfied by existing data. For the baryon decouplet, it predicted an equal mass spacing between members.
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August 25, 2025 at 1:21 PM
a symmetry-breaking term, provides a way to calculate the mass of a particle within an SU(3) multiplet.
For the baryon octet, the formula yielded a mass relation that was well-satisfied by existing data. For the baryon decouplet, it predicted an equal mass spacing between members.
8/
For the baryon octet, the formula yielded a mass relation that was well-satisfied by existing data. For the baryon decouplet, it predicted an equal mass spacing between members.
8/
that all hadrons were bound states of three elementary particles: the proton (p), neutron (n), and Lambda (Λ).
Susumu Okubo noted that this approach was awkward for certain baryons.
Okubo's main contribution was providing a successful mass formula for the SU(3) theory.
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Susumu Okubo noted that this approach was awkward for certain baryons.
Okubo's main contribution was providing a successful mass formula for the SU(3) theory.
7/
August 25, 2025 at 1:20 PM
that all hadrons were bound states of three elementary particles: the proton (p), neutron (n), and Lambda (Λ).
Susumu Okubo noted that this approach was awkward for certain baryons.
Okubo's main contribution was providing a successful mass formula for the SU(3) theory.
7/
Susumu Okubo noted that this approach was awkward for certain baryons.
Okubo's main contribution was providing a successful mass formula for the SU(3) theory.
7/
and as bound states of one another. While influential, it didn't provide enough progress for hadron spectroscopy.
People working on the Reductionist Approach proposed that hadrons were bound states of simpler, fundamental objects. Shoichi Sakata's model, for instance, proposed
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People working on the Reductionist Approach proposed that hadrons were bound states of simpler, fundamental objects. Shoichi Sakata's model, for instance, proposed
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August 25, 2025 at 1:19 PM
and as bound states of one another. While influential, it didn't provide enough progress for hadron spectroscopy.
People working on the Reductionist Approach proposed that hadrons were bound states of simpler, fundamental objects. Shoichi Sakata's model, for instance, proposed
6/
People working on the Reductionist Approach proposed that hadrons were bound states of simpler, fundamental objects. Shoichi Sakata's model, for instance, proposed
6/
This approach led to the successful concept of unitary symmetry, now known as flavor-SU(3) theory, introduced by Gell-Mann, Yuval Ne'eman, and Yoshio Yamaguchi.
In the Nuclear Democracy approach, based on S-matrix theory, all hadrons are considered as equally elementary
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In the Nuclear Democracy approach, based on S-matrix theory, all hadrons are considered as equally elementary
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August 25, 2025 at 1:18 PM
This approach led to the successful concept of unitary symmetry, now known as flavor-SU(3) theory, introduced by Gell-Mann, Yuval Ne'eman, and Yoshio Yamaguchi.
In the Nuclear Democracy approach, based on S-matrix theory, all hadrons are considered as equally elementary
5/
In the Nuclear Democracy approach, based on S-matrix theory, all hadrons are considered as equally elementary
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Several approaches emerged: the Group theoretical approach, "Nuclear Democracy" (of Chew et al.) and the Reductionist Approach.
In the first approach, physicists aimed to find a larger symmetry group containing SU(2)⊗U(1), that would approximately describe strong interactions.
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In the first approach, physicists aimed to find a larger symmetry group containing SU(2)⊗U(1), that would approximately describe strong interactions.
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August 25, 2025 at 1:17 PM
Several approaches emerged: the Group theoretical approach, "Nuclear Democracy" (of Chew et al.) and the Reductionist Approach.
In the first approach, physicists aimed to find a larger symmetry group containing SU(2)⊗U(1), that would approximately describe strong interactions.
4/
In the first approach, physicists aimed to find a larger symmetry group containing SU(2)⊗U(1), that would approximately describe strong interactions.
4/
However, by the 1950s, many new hadrons, like kaons and "strange" baryons (e.g., Λ and Σ), were discovered. To account for their properties, a new quantum number called hypercharge (Y) was introduced.
This led to a larger group, SU(2) ⊗ U(1).
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This led to a larger group, SU(2) ⊗ U(1).
3/
August 25, 2025 at 1:16 PM
However, by the 1950s, many new hadrons, like kaons and "strange" baryons (e.g., Λ and Σ), were discovered. To account for their properties, a new quantum number called hypercharge (Y) was introduced.
This led to a larger group, SU(2) ⊗ U(1).
3/
This led to a larger group, SU(2) ⊗ U(1).
3/
in cosmic rays, the list of known particles expanded to include muons and pions. The similar masses of the proton and neutron, as well as those of the three pions (π⁺, π⁰,π⁻), led to the idea of isotopic-spin invariance of strong interactions, represented by the SU(2) group.
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August 25, 2025 at 1:16 PM
in cosmic rays, the list of known particles expanded to include muons and pions. The similar masses of the proton and neutron, as well as those of the three pions (π⁺, π⁰,π⁻), led to the idea of isotopic-spin invariance of strong interactions, represented by the SU(2) group.
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