Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Maciej Dunajski"'
Publikováno v:
Physics Letters B, Vol 859, Iss , Pp 139097- (2024)
We determine the frequency ratios τ≡ωz/ωρ for which the Hamiltonian system with a potentialV=1r+12(ωρ2(x2+y2)+ωz2z2) is completely integrable. We relate this result to the existence of conformal Killing tensors of the associated Eisenhart me
Externí odkaz:
https://doaj.org/article/e03c6450443943cc9a5f4c3542d519b7
Publikováno v:
Physics Letters B, Vol 780, Iss , Pp 166-168 (2018)
We construct a new class of solutions to the dispersionless hyper-CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein–Maxwell cosmological space–time in (3+1)-dimensions.
Externí odkaz:
https://doaj.org/article/b1056b4323e54310a140e3374b73a745
Autor:
Maciej Dunajski
Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and i
Autor:
Maciej Dunajski, Roger Penrose
Publikováno v:
Annals of Physics. 451:169243
We discuss the equivalence principle in quantum mechanics in the context of Newton--Cartan geometry, and non--relativistic twistor theory.
Comment: 14 pages, one figure. Final version, published in the Annals of Physics
Comment: 14 pages, one figure. Final version, published in the Annals of Physics
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ee994ea3f3011a2d6fa3d373d96abb0
https://doi.org/10.1016/j.aop.2023.169243
https://doi.org/10.1016/j.aop.2023.169243
Autor:
Maciej Dunajski
‘Other geometries’ offers an overview of some modern geometries and their links with other areas of mathematics, such as Gauss lemma in number theory and Gaussian distributions in statistics. The Atiyah–Singer index theorem, proved in 1963 by M
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a3b592648ac9ad27f9101672d34c496b
https://doi.org/10.1093/actrade/9780199683680.003.0006
https://doi.org/10.1093/actrade/9780199683680.003.0006
Autor:
Maciej Dunajski
‘What is geometry?’ mentions the Greek philosopher Pythagoras of Samos and his followers, the Pythagoreans, who spent their time unveiling the relationship between numbers and geometric forms. They were credited for what is now known as the Pytha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e597f2cc0d582bf9216bbef26a39ec24
https://doi.org/10.1093/actrade/9780199683680.003.0001
https://doi.org/10.1093/actrade/9780199683680.003.0001
Autor:
Maciej Dunajski
‘Euclidean geometry’ talks about the cultures that grew up in the arid region of Mesopotamia in the fourth millennium BC that needed to find geometrical solutions to their problems. Dividing and surveying the land after periodic floods relied on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f26553231ca449e4a2aee904afdd6297
https://doi.org/10.1093/actrade/9780199683680.003.0002
https://doi.org/10.1093/actrade/9780199683680.003.0002
Autor:
Maciej Dunajski
‘Non-Euclidean geometry’ begins with a discussion on spherical geometry, which is the study of objects on the sphere and has lines that are defined as great circles. Spherical geometry is an example of a non-Euclidean geometry, as the lines do no
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::63e13f22bfe5289d4a73200c9dcf187f
https://doi.org/10.1093/actrade/9780199683680.003.0003
https://doi.org/10.1093/actrade/9780199683680.003.0003
Autor:
Maciej Dunajski
Geometry: A Very Short Introduction discusses the fundaments of Euclidean and non-Euclidean geometries. This topic includes curved spaces, projective geometry in Renaissance art, and the geometry of spacetime inside a black hole. The study of geometr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7b381736d57925fc86646a0802c5aa19
https://doi.org/10.1093/actrade/9780199683680.001.0001
https://doi.org/10.1093/actrade/9780199683680.001.0001
Autor:
Maciej Dunajski
‘Geometry of the physical world’ reviews Euclidean geometry, which provided a framework for interpreting empirical observations and making accurate predictions for over two millennia. However, as measuring apparatus improved, the geometry of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::42157bfdfe642353c58e7084ecac2aac
https://doi.org/10.1093/actrade/9780199683680.003.0007
https://doi.org/10.1093/actrade/9780199683680.003.0007