Spinors in Hilbert Space (eBook)

Paul Dirac (Autor)

eBook Download: PDF

2012
Springer US (Verlag)
978-1-4757-0034-3 (ISBN)

Infos

1. Hilbert Space The words "e;Hilbert space"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 6.12.2012
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• ISBN-10: 1-4757-0034-2 / 1475700342
• ISBN-13: 978-1-4757-0034-3 / 9781475700343