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# 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.

• Introduction

Pages 3-4

Dirac, P. A. M.

• Finite Number of Dimensions

Pages 5-32

Dirac, P. A. M.

• Even Number of Dimensions

Pages 33-56

Dirac, P. A. M.

• Infinite Number of Dimensions

Pages 57-91

Dirac, P. A. M.

eBook 74,89 €
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
Softcover 93,59 €
price for Spain (gross)
• ISBN 978-1-4757-0036-7
• Free shipping for individuals worldwide
• Institutional customers should get in touch with their account manager
• Covid-19 shipping restrictions
• Usually ready to be dispatched within 3 to 5 business days, if in stock
• The final prices may differ from the prices shown due to specifics of VAT rules

## Bibliographic Information

Bibliographic Information
Book Title
Spinors in Hilbert Space
Authors
1974
Publisher
Springer US
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