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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)
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Introduction
Pages 3-4
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Finite Number of Dimensions
Pages 5-32
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Even Number of Dimensions
Pages 33-56
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Infinite Number of Dimensions
Pages 57-91
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Table of contents (4 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Spinors in Hilbert Space
- Authors
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- Paul Dirac
- 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
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