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Spinors in Hilbert Space

Paul Dirac (Autor)

Buch | Hardcover

98 Seiten

1975
Kluwer Academic / Plenum Publishers (Verlag)
978-0-306-30798-0 (ISBN)

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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.

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.

Zusatzinfo	1 black & white illustrations, biography
Verlagsort	Dordrecht
Sprache	englisch
Maße	150 x 240 mm
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	0-306-30798-7 / 0306307987
ISBN-13	978-0-306-30798-0 / 9780306307980
Zustand	Neuware