On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

Foldy, L. L.; Wouthuysen, S. A.

doi:10.1103/physrev.78.29

Cited by 2,128 publications

(1,791 citation statements)

References 4 publications

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“…An expansion in v can be performed by expanding the Dirac fields with fields of NRQCD. This can be done by using Foldy-Wouthuysen transformation [16]:…”

Section: The Correction At the Next-to Leading Ordermentioning

confidence: 99%

Corrections for two photon decays of χc0 and χc2 and color octet contributions

Ma¹,

Wang²

2002

Physics Letters B

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Using the fact that the c-quark inside a charmonium moves with a small velocity v in the charmonium rest-frame, one can employ an expansion in v to study decays of charmonia and results at the leading order for χc0,2 → γγ exist in the literature. We study corrections at the next-to-leading order in the framework of nonrelativistic QCD(NRQCD) factorization. The study presented here is different than previous approaches where χc0,2 is taken as a bound-state of a cc pair and a nonrelativistic wave-function is used for the pair. We find that the corrections are consist not only of relativistic corrections, but also of corrections from Fock state components of χc0,2 in which the cc pair is in a color-octet state. For χc2 there is also a contribution from a Fock state component in which the pair is in a F-wave state. We determine the factorization formula for decay widths in the form of NRQCD matrix elements representing nonperturbative effects related to χc0,2, and calculate the perturbative coefficients at tree-level. Because the NRQCD matrix elements are unknown, a detailed prediction for the decay χc0,2 → γγ can not be made, but the effect of these corrections can be determined at certain level. Estimations show that the effect is significant and can not be neglected.

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“…An expansion in v can be performed by expanding the Dirac fields with fields of NRQCD. This can be done by using Foldy-Wouthuysen transformation [16]:…”

Section: The Correction At the Next-to Leading Ordermentioning

confidence: 99%

Corrections for two photon decays of χc0 and χc2 and color octet contributions

Ma¹,

Wang²

2002

Physics Letters B

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“…The CT method has been extensively used, even outside condensed matter physics. For example, Foldy and Wouthuysen employed the CT to derive the lowest order relativistic corrections to the Schrödinger equation, starting from the Dirac equation 8 . Two of the best known applications of the CT in condensed matter physics are the derivation of the Kondo model from the Anderson impurity model using the Schrieffer-Wolff CT 9 and the derivation, starting from the Hubbard model of an exchange spin Hamiltonian with ring/cyclic exchange terms 1,2,3 .…”

Section: Introductionmentioning

confidence: 99%

Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

et al. 2005

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We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U ) to intermediate coupling limit (i.e. away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U ) 3 . We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U → 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S = 1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U , despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U . We also comment on quantitative aspects of the t/U and 1/S expansions.

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“…Then the physical meaning of the operator p i became rather obscure in both the semiclassical and the RQM framework. Using the quantum-fieldtheory arguments, Foldy and Wouthuysen [6] argued that the basic operator x which appears in the Dirac equation does not correspond to the observable quantity. Then they constructed the position operator X i with reasonable properties.…”

Section: Conclusion Pseudo-classical Mechanics and The Classicalmentioning

confidence: 99%

“…Although a true understanding of spin is achieved in the framework of quantum electrodynamics, a lot of effort has been spent in attempts to construct a mechanical model of a spinning electron, see [1][2][3][4][5][6][7][8][9][10][11][15][16][17] and references therein. The Dirac spinor Ψ can be used to construct the four-dimensional current vector,Ψγ µ Ψ, which preserves for solutions to the Dirac equation, ∂ µ (Ψγ µ Ψ) = 0.…”

Section: Conclusion Pseudo-classical Mechanics and The Classicalmentioning

confidence: 99%