{"product_id":"9781475700367","title":"Spinors in Hilbert Space","description":"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.","brand":"Paul Dirac","offers":[{"title":"Default Title","offer_id":46784274104638,"sku":"9781475700367","price":3001.1,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781475700367_dfb5f049-0b72-4cdd-8544-9a06bc203460.jpg?v=1707479723","url":"https:\/\/exclusivebooks.co.za\/products\/9781475700367","provider":"Exclusive Books Online","version":"1.0","type":"link"}