{"product_id":"spinors-in-hilbert-space-paul-dirac-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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Paul Dirac\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1475700369\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781475700367\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/02\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 91\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.32lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.21d","brand":"Paul Dirac","offers":[{"title":"Paperback","offer_id":44860411773183,"sku":"9781475700367","price":119.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_e6fc34c7-5627-4174-a7e5-5c464a38e914.jpg?v=1709136018","url":"https:\/\/www.whiterainbookhouse.com\/products\/spinors-in-hilbert-space-paul-dirac-9781475700367","provider":"WR Book House","version":"1.0","type":"link"}