The zitterbewegung interpretation of quantum mechanics

Hestenes, David

doi:10.1007/bf01889466

Cited by 211 publications

(227 citation statements)

References 13 publications

(18 reference statements)

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“…Schrödinger noticed that if a mathematical superposition state of positive and negative energies were evolved in time according to the single-particle Dirac equation, then the time-dependent expectation value of the position operator in this mathematical state reveals oscillatory motion with a speed of light, a period of¯h mc 2 , and an amplitude proportional to the reduced Compton wavelength (¯h mc ) as a result of the interference between positive-and negativeenergy states. The Zitterbewegung is often presented as if it refers to an observable trembling motion associated with a real physical particle [6,7]; for example, it was suggested as the origin of the electron spin [8], and it is given as a reasoning for the Darwin term [9] in atomic fine structure. However, this concept is controversial and was challenged by Krekora et al [10].…”

Section: Introductionmentioning

confidence: 99%

Propagation of a relativistic electron wave packet in the Dirac equation

Park

2012

Phys. Rev. A

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Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.

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Section: Introductionmentioning

confidence: 99%

Propagation of a relativistic electron wave packet in the Dirac equation

Park

2012

Phys. Rev. A

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“…He introduced an equation, now known as the Dirac-Hestenes equation, which does not contains (explicitly) imaginary numbers and obtained a very clever interpretation of that theory through the study of the geometrical meaning of the so called bilinear covariants, which are the observables of the theory. He further developed an interpretation of quantum theory from his formalism [88,89], that he called the zitterbewegung interpretation. Also, he showed how his approach it suggests a geometrical link between electromagnetism and the weak interactions, different from the original one of the standard model [87] Hestenes papers and his book with Sobczyk [86] have been the inspiration for a series of international conferences on 'Clifford Algebras and their Applications in Mathematical Physics' which in 2002 have had its sixth edition.…”

Section: Introductionmentioning

confidence: 99%

Algebraic and Dirac–Hestenes spinors and spinor fields

Rodrigues

2004

Journal of Mathematical Physics

122

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Almost all presentations of Dirac theory in first or second quantization in Physics (and Mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of non homogeneous even multivectors fields) is used. However, a carefully analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF ) and Dirac-Hestenes spinor fields (DHSF ) on Minkowski spacetime as some equivalence classes of pairs (Ξu, ψ Ξu ), where Ξu is a spinorial frame field and ψ Ξu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a carefull analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the 'bilinear covariants' (on Minkowski spacetime) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary RiemannCartan spacetimes. The present paper contains also Appendices (A-E) which exhibits a truly useful collection of results concerning the theory of

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“…The argument in support of these contentions has been elaborated elsewhere [3], so we can be satisfied here with an outline of the main ideas. The argument and its implications are developed in three separate stages.…”

Section: Introductionmentioning

confidence: 82%

The Kinematic Origin of Complex Wave Functions

Hestenes¹

1993

Physics and Probability

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Abstract.A reformulation of the Dirac theory reveals that ih has a geometric meaning relating it to electron spin. This provides the basis for a coherent physical interpretation of the Dirac and Schödinger theories wherein the complex phase factor exp(−iϕ/h) in the wave function describes electron zitterbewegung, a localized, circular motion generating the electron spin and magnetic moment. Zitterbewegung interactions also generate resonances which may explain quantization, diffraction, and the Pauli principle.

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The zitterbewegung interpretation of quantum mechanics

Cited by 211 publications

References 13 publications

Propagation of a relativistic electron wave packet in the Dirac equation

Propagation of a relativistic electron wave packet in the Dirac equation

Algebraic and Dirac–Hestenes spinors and spinor fields

The Kinematic Origin of Complex Wave Functions

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