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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Physics Mathematical physics

• Full title: Spinors in Hilbert Space
• Author: Paul Dirac
• Language: English
• Binding: Paperback
• Number of pages: 91
• EAN: 9781475700367
• ISBN: 1475700369
• ID: 05258345
• Publisher: Springer-Verlag New York Inc.
• Weight: 162 g
• Dimensions: 229 × 153 × 6 mm
• Date of publishing: 02. May 2012

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