{"product_id":"9781475700367","title":"Spinors in Hilbert Space","description":"\u003ch1\u003eSpinors in Hilbert Space\u003c\/h1\u003e \u003ch2\u003eDirac, Paul\u003c\/h2\u003e \u003cp\u003e1. 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-05-02\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781475700367\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4757-0034-3\u003c\/p\u003e \u003cp\u003eDimensions: 229.0cm x152.0cm\u003c\/p\u003e \u003cp\u003ePages: 91.0\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":44479056969868,"sku":"9781475700367","price":107.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781475700367.jpg?v=1757598673","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781475700367","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}