Paul Dirac

Spinors in Hilbert Space (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 91
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781475700343
• Artikelnr.: 43994226

Inhaltsangabe

1. Hilbert Space.- 2. Spinors.- Finite Number of Dimensions.- 3. Rotations in n Dimensions.- 4. Null Vectors and Null Planes.- 5. The Independence Theorem.- 6. Specification of a Null Plane without Its Coordinates.- 7. Matrix Notation.- 8. Expression of a Rotation in Terms of an Infinitesimal Rotation.- 9. Complex Rotations.- 10. The Noncommutative Algebra.- 11. Rotation Operators.- 12. Fixation of the Coefficients of Rotation Operators.- 13. The Ambiguity of Sign.- 14. Kets and Bras.- 15. Simple Kets.- Even Number of Dimensions.- 16. The Ket Matrix.- 17. The Two-Ket-Matrix Theorem.- 18. The Connection between Two Ket Matrices.- 19. The Representation of Kets.- 20. The Representative of a Simple Ket. General.- 21. The Representative of a Simple Ket. Special Cases.- 22. Fixation of the Coefficients of Simple Kets.- 23. The Scalar Product Formula.- Infinite Number of Dimensions.- 24. The Need for Bounded Matrices.- 25. The Infinite Ket Matrix.- 26. Passage from One Ket Matrix to Another.- 27. The Various Kinds of Ket Matrices.- 28. Failure of the Associative Law.- 29. The Fundamental Commutators.- 30. Boson Variables.- 31. Boson Emission and Absorption Operators.- 32. Infinite Determinants.- 33. Validity of the Scalar Product Formula.- 34. The Energy of a Boson.- 35. Physical Application.