{"product_id":"spinors-in-hilbert-space-von-paul-dirac","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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781475700367\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9781475700367","offer_id":39417381879901,"sku":"9781475700367","price":117.69,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/c6bf8cd9-30ce-4580-ac30-8f927725e0a8.jpg?v=1756959298","url":"https:\/\/shop.autorenwelt.de\/en\/products\/spinors-in-hilbert-space-von-paul-dirac","provider":"Autorenwelt Shop","version":"1.0","type":"link"}