“The spinor genus is due to Eichler. His early results (1952) established the theory over the rational field and also, in certain special cases, over a number field. Kneser (1956) extended this to number fields in general. At about the same time Watson obtained Eichler's results by elementary methods over the rational field.”

— O. Timothy O'Meara

[Review: Integral quadratic forms by G. L. Watson, Bull. Amer. Math. Soc., 67, 1961, 536–538, 10.1090/S0002-9904-1961-10673-3] (quote from p. 537)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The spinor genus is due to Eichler. His early results (1952) established the theory over the rational field and also, i…" by O. Timothy O'Meara?

O. Timothy O'Meara 3

American mathematician 1928–2018

Related quotes

“It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex.”

Freeman Dyson (1923) theoretical physicist and mathematician

[The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics, Jour. Math. Phys., 3, 1962, 1199–1215, https://books.google.com/books?id=nnyNUidX1OMC&pg=PA410] (p. 1200)

“In a previous paper we showed that a static (nonrotating) black hole cannot be endowed with exterior scalar-meson or massive vector-meson fields. Here we show that the same is true for massive spin-2 meson fields. We also extend the above results to the case of a rotating stationary black hole. We conclude from our results that a black hole in its final (static or stationary) state cannot interact with the exterior world via the strong interactions which are mediated by meson fields such as the π (scalar), ρ (vector), and ƒ (spin-2). A direct consequence of this is the impossibility of determining the baryon number of the black hole by means of exterior measurements alone. This results in the transcendence of the law of baryon-number conservation as originally predicted by Wheeler.”

Jacob Bekenstein (1947–2015) Mexican-Israeli physicist

[Nonexistence of baryon number for black holes. II, Physical Review D, 5, 10, 15 May 1972, 2403–2412, 10.1103/PhysRevD.5.2403]

“When the theory performs well you also think, “Are there parallel results in naturally occurring field data?” You look for coherence across different data sets because theories are not specific to particular data sources. Such extensions are important because theories often make specific assumptions about information and institutions which can be controlled in the laboratory, but which may not accurately represent field data generating situations. Testing theories on the domain of their assumptions is sterile unless it is part of a research program concerned with extending the domain of applications of theory to field environments”

Vernon L. Smith (1927) American economist

Source: "Theory, experiment and economics," 1989, p. 151.

“Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2).”

John Henry Schwarz (1941) American theoretical physicist

p. 1

“We have known since the middle of the nineteenth century that the world is not composed only of particles. …the world is also composed of fields. …General relativity is a theory of… the gravitational field. …Because there are three sets of field lines, the gravitational field defines a network of relationships having to do with how the… lines link with one another. …This is why we call relativity a relational theory.”

Lee Smolin book Three Roads to Quantum Gravity

Three Roads to Quantum Gravity (2000)

“We are confident that the Islamic logic, culture, and discourse can prove their superiority in all fields over all schools of thought and theories.”

Mahmoud Ahmadinejad (1956) 6th President of the Islamic Republic of Iran

Ahmadinejad on His Proposal for a Jewish State in Europe and on Iran's Nuclear Energy http://www.memritv.org/Transcript.asp?P1=987 Jan. 2006.
2006

“It’s past time that people get involved in thinking – now that the computers can take over the field of memory.”

Eugene J. Martin (1938–2005) American artist

Annotated Drawings by Eugene J. Martin: 1977-1978

“Faint winds, and far away a fading laughter…
And the rain and over the fields a voice calling…”

F. Scott Fitzgerald (1896–1940) American novelist and screenwriter

Quoted, This Side of Paradise (1920)

“What lead me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Letter to the Michelson Commemorative Meeting of the Cleveland Physics Society (1952), as quoted by R.S.Shankland, Am J Phys 32, 16 (1964), p35, republished in A P French, Special Relativity, ISBN 0177710756
1950s

“For like a poisonous breath over the fields, like a mass of locusts over Egypt, so the swarm of excuses is a general plaque, a ruinous infection among men, that eats off the sprouts of the Eternal.”

Sören Kierkegaard (1813–1855) Danish philosopher and theologian, founder of Existentialism

Help us to complete the source, original and additional information

O. Timothy O'Meara 3

Related quotes

Related topics