Precisely Predictable Dirac Observables (Hardcover)

Heinz Otto Cordes

ISBN 10: 1402051689 / ISBN 13: 9781402051685

Editore: Springer-Verlag New York Inc., New York, NY, 2006

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Hardcover. In this book we are attempting to o?er a modi?cation of Diracs theory of the electron we believe to be free of the usual paradoxa, so as perhaps to be acceptable as a clean quantum-mechanical treatment. While it seems to be a fact that the classical mechanics, from Newton to E- steins theory of gravitation, o?ers a very rigorous concept, free of contradictions and able to accurately predict motion of a mass point, quantum mechanics, even in its simplest cases, does not seem to have this kind of clarity. Almost it seems that everyone of its fathers had his own wave equation. For the quantum mechanical 1-body problem (with vanishing potentials) let 1 us focus on 3 di?erent wave equations : (I) The Klein-Gordon equation 3 2 2 2 2 (1) ? ?/?t +(1??)? =0 , ? = Laplacian = ? /?x . j 1 This equation may be written as ? ? (2) (?/?t?i 1??)(?/?t +i 1??)? =0 . Hereitmaybenotedthattheoperator1??hasawellde?nedpositive square root as unbounded self-adjoint positive operator of the Hilbert 2 3 spaceH = L (R ). For the quantum mechanical 1-body problem (with vanishing potentials) let 1 us focus on 3 di?erent wave equations : (I) The Klein-Gordon equation 3 2 2 2 2 (1) ? =0 , ? = Laplacian = ? Hereitmaybenotedthattheoperator1??hasawellde?nedpositive square root as unbounded self-adjoint positive operator of the Hilbert 2 3 spaceH = L (R ). Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781402051685

Dati bibliografici

• Titolo: Precisely Predictable Dirac Observables (Hardcover)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 1402051689
• ISBN 13: 9781402051685
• Rilegatura: Hardcover
• Condizione: new

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Riassunto

This work presents a Clean Quantum Theory of the Electron, based on Dirac’s equation. "Clean" in the sense of a complete mathematical explanation of the well known paradoxes of Dirac’s theory and a connection to classical theory. It discusses the existence of an accurate split between physical states belonging to the electron and to the positron as well as the fact that precisely predictable observables must preserve this split.

Dalla quarta di copertina

This work presents a "Clean Quantum Theory of the Electron", based on Dirac s equation. "Clean" in the sense of a complete mathematical explanation of the well known paradoxes of Dirac s theory, and a connection to classical theory, including the motion of a magnetic moment (spin) in the given field, all for a charged particle (of spin ½) moving in a given electromagnetic field.
This theory is relativistically covariant, and it may be regarded as a mathematically consistent quantum-mechanical generalization of the classical motion of such a particle, à la Newton and Einstein. Normally, our fields are time-independent, but also discussed is the time-dependent case, where slightly different features prevail. A "Schroedinger particle", such as a light quantum, experiences a very different (time-dependent) "Precise Predictablity of Observables". An attempt is made to compare both cases. There is not the Heisenberg uncertainty of location and momentum; rather, location alone possesses a built-in uncertainty of measurement.
Mathematically, our tools consist of the study of a pseudo-differential operator (i.e. an "observable") under conjugation with the Dirac propagator: such an operator has a "symbol" approximately propagating along classical orbits, while taking its "spin" along. This is correct only if the operator is "precisely predictable", that is, it must approximately commute with the Dirac Hamiltonian, and, in a sense, will preserve the subspaces of electronic and positronic states of the underlying Hilbert space.

Audience:
Theoretical Physicists, specifically in Quantum Mechanics.
Mathematicians, in the fields of Analysis, Spectral Theory of Self-adjoint differential operators, and Elementary Theory of Pseudo-Differential Operators