Overview
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (4 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Spinors in Hilbert Space
Authors: P. A. M. Dirac
DOI: https://doi.org/10.1007/978-1-4757-0034-3
Publisher: Springer New York, NY
-
eBook Packages: Springer Book Archive
Copyright Information: Plenum Press, New York 1974
Softcover ISBN: 978-1-4757-0036-7Published: 02 May 2012
eBook ISBN: 978-1-4757-0034-3Published: 06 December 2012
Edition Number: 1
Number of Pages: VII, 91
Number of Illustrations: 1 b/w illustrations