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| Author | : Roger Plymen |
| Publisher | : Cambridge University Press |
| Total Pages | : 192 |
| Release | : 1994-12 |
| Genre | : Mathematics |
| ISBN | : 9780521450225 |
A definitive self-contained account of the subject. Of appeal to a wide audience in mathematics and physics.
| Author | : Paul Dirac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 97 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1475700342 |
1. Hilbert Space The words "Hilbert space" here will always denote what math ematicians call a separable Hilbert space. It is composed of vectors each with a denumerable infinity of coordinates ql' q2' Q3, .... Usually the coordinates are considered to be complex numbers and each vector has a squared length ~rIQrI2. This squared length must converge in order that the q's may specify a Hilbert vector. Let us express qr in terms of real and imaginary parts, qr = Xr + iYr' Then the squared length is l:.r(x; + y;). The x's and y's may be looked upon as the coordinates of a vector. It is again a Hilbert vector, but it is a real Hilbert vector, with only real coordinates. Thus a complex Hilbert vector uniquely determines a real Hilbert vector. The second vector has, at first sight, twice as many coordinates as the first one. But twice a denumerable in finity is again a denumerable infinity, so the second vector has the same number of coordinates as the first. Thus a complex Hilbert vector is not a more general kind of quantity than a real one.
| Author | : Élie Cartan |
| Publisher | : Courier Corporation |
| Total Pages | : 193 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486137325 |
Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities.
| Author | : Katharina Habermann |
| Publisher | : Springer |
| Total Pages | : 131 |
| Release | : 2006-10-28 |
| Genre | : Mathematics |
| ISBN | : 3540334211 |
This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research.
| Author | : Rafal Ablamowicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 428 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401584222 |
This volume is dedicated to the memory of Albert Crumeyrolle, who died on June 17, 1992. In organizing the volume we gave priority to: articles summarizing Crumeyrolle's own work in differential geometry, general relativity and spinors, articles which give the reader an idea of the depth and breadth of Crumeyrolle's research interests and influence in the field, articles of high scientific quality which would be of general interest. In each of the areas to which Crumeyrolle made significant contribution - Clifford and exterior algebras, Weyl and pure spinors, spin structures on manifolds, principle of triality, conformal geometry - there has been substantial progress. Our hope is that the volume conveys the originality of Crumeyrolle's own work, the continuing vitality of the field he influenced, and the enduring respect for, and tribute to, him and his accomplishments in the mathematical community. It isour pleasure to thank Peter Morgan, Artibano Micali, Joseph Grifone, Marie Crumeyrolle and Kluwer Academic Publishers for their help in preparingthis volume.
| Author | : Paul Adrien Maurice Dirac |
| Publisher | : |
| Total Pages | : 200 |
| Release | : 1970 |
| Genre | : Hilbert space |
| ISBN | : |
| Author | : Pertti Lounesto |
| Publisher | : Cambridge University Press |
| Total Pages | : 352 |
| Release | : 2001-05-03 |
| Genre | : Mathematics |
| ISBN | : 0521005515 |
This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
| Author | : Andrzej Borowiec |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401117195 |
ZBIGNIEW OZIEWICZ University of Wroclaw, Poland December 1992 The First Max Born Symposium in Theoretical and Mathematical Phy sics, organized by the University of Wrodaw, was held in September 1991 with the intent that it would become an annual event. It is the outgrowth of the annual Seminars organized jointly since 1972 with the University of Leipzig. The name of the Symposia was proposed by Professor Jan Lopu szanski. Max Born, an outstanding German theoretical physicist, was born in 1883 in Breslau (the German name of Wrodaw) and educated here. The Second Max Born Symposium was held during the four days 24- 27 September 1992 in an old Sobotka Castle 30 km west of Wrodaw. The Sobotka Castle was built in the eleventh century. The dates engraved on the walls of the Castle are 1024, 1140, and at the last rebuilding, 1885. The castle served as a cloister until the end of the sixteenth century.
| Author | : Giuseppe Furlan |
| Publisher | : World Scientific |
| Total Pages | : 368 |
| Release | : 1988-11-01 |
| Genre | : |
| ISBN | : 9814644447 |
This conference brought together physicists and mathematicians working on spinors, which have played an important role in recent research on supersymmetry, Kaluza-Klein theories, twistors and general relativity.
| Author | : Guido Fano |
| Publisher | : Springer |
| Total Pages | : 283 |
| Release | : 2017-06-27 |
| Genre | : Science |
| ISBN | : 3319587323 |
This book is designed to make accessible to nonspecialists the still evolving concepts of quantum mechanics and the terminology in which these are expressed. The opening chapters summarize elementary concepts of twentieth century quantum mechanics and describe the mathematical methods employed in the field, with clear explanation of, for example, Hilbert space, complex variables, complex vector spaces and Dirac notation, and the Heisenberg uncertainty principle. After detailed discussion of the Schrödinger equation, subsequent chapters focus on isotropic vectors, used to construct spinors, and on conceptual problems associated with measurement, superposition, and decoherence in quantum systems. Here, due attention is paid to Bell’s inequality and the possible existence of hidden variables. Finally, progression toward quantum computation is examined in detail: if quantum computers can be made practicable, enormous enhancements in computing power, artificial intelligence, and secure communication will result. This book will be of interest to a wide readership seeking to understand modern quantum mechanics and its potential applications.
