SULJE VALIKKO

avaa valikko

Variations on a Theme by Kepler
89,50 €
American Mathematical Society
Asu: Pehmeäkantinen kirja
Julkaisuvuosi: 2006, 30.09.2006 (lisätietoa)
Kieli: Englanti
This book is based on the Colloquium Lectures presented by Shlomo Sternberg in 1990. The authors delve into the mysterious role that groups, especially Lie groups, play in revealing the laws of nature by focusing on the familiar example of Kepler motion: the motion of a planet under the attraction of the sun according to Kepler's laws. Newton realized that Kepler's second law--that equal areas are swept out in equal times--has to do with the fact that the force is directed radially to the sun. Kepler's second law is really the assertion of the conservation of angular momentum, reflecting the rotational symmetry of the system about the origin of the force. In today's language, we would say that the group $O(3)$ (the orthogonal group in three dimensions) is responsible for Kepler's second law. By the end of the nineteenth century, the inverse square law of attraction was seen to have $O(4)$ symmetry (where $O(4)$ acts on a portion of the six-dimensional phase space of the planet). Even larger groups h The remainder of the book is aimed at specialists.It begins with a demonstration that the Kepler problem and the hydrogen atom exhibit $O(4)$ symmetry and that the form of this symmetry determines the inverse square law in classical mechanics and the spectrum of the hydrogen atom in quantum mechanics. The space of regularized elliptical motions of the Kepler problem (also known as the Kepler manifold) plays a central role in this book. The last portion of the book studies the various cosmological models in this same conformal class (and having varying isometry groups) from the viewpoint of projective geometry. The computation of the hydrogen spectrum provides an illustration of the principle that enlarging the phase space can simplify the equations of motion in the classical setting and aid in the quantization problem in the quantum setting. The authors provide a short summary of the homological quantization of constraints and a list of recent applications to many interesting finite-dimensional set

Tuotetta lisätty
ostoskoriin kpl
Siirry koriin
LISÄÄ OSTOSKORIIN
Tuotteella on huono saatavuus ja tuote toimitetaan hankintapalvelumme kautta. Tilaamalla tämän tuotteen hyväksyt palvelun aloittamisen. Seuraa saatavuutta.
Myymäläsaatavuus
Helsinki
Tapiola
Turku
Tampere
Variations on a Theme by Kepler
Näytä kaikki tuotetiedot
ISBN:
9780821841846
Sisäänkirjautuminen
Kirjaudu sisään
Rekisteröityminen
Oma tili
Omat tiedot
Omat tilaukset
Omat laskut
Lisätietoja
Asiakaspalvelu
Tietoa verkkokaupasta
Toimitusehdot
Tietosuojaseloste