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Spinors in Hilbert Space by Paul Dirac

Spinors in Hilbert Space

by Paul Dirac
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Book cover type: Paperback
  • ISBN13: 9781475700367
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 91
  • Original Price: EUR 109.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 156 grams
  • BISAC Subject(s): Physics / Mathematical & Computational

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.

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