Spinors in Hilbert Space

Authors: Dirac, Paul

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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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook 74,96 €
price for Spain (gross)
  • ISBN 978-1-4757-0034-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 93,59 €
price for Spain (gross)
  • ISBN 978-1-4757-0036-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Spinors in Hilbert Space
Authors
Copyright
1974
Publisher
Springer US
Copyright Holder
Plenum Press, New York
eBook ISBN
978-1-4757-0034-3
DOI
10.1007/978-1-4757-0034-3
Softcover ISBN
978-1-4757-0036-7
Edition Number
1
Number of Pages
VII, 91
Number of Illustrations
1 b/w illustrations
Topics