Polarization effects in the positron theory
TL;DR: In this paper, the positron theory for the special case of impressed electrostatic fields is investigated and the existence of an induced charge corresponds to a polarization of the vacuum, and as a consequence, to deviations from Coulomb's law for the mutual potential energy of point charges.
Abstract: Some of the consequences of the positron theory for the special case of impressed electrostatic fields are investigated. By imposing a restriction only on the maximum value of the field intensity, which must always be assumed much smaller than a certain critical value, but with no restrictions on the variation of this intensity, a formula for the charge induced by a charge distribution is obtained. The existence of an induced charge corresponds to a polarization of the vacuum, and as a consequence, to deviations from Coulomb's law for the mutual potential energy of point charges. Consequences of these deviations which are investigated are the departures from the Coulombian scattering law for heavy particles and the displacement in the energy levels for atomic electrons moving in the field of the nucleus.
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TL;DR: In this paper, the authors compared Dirac's theory of the positron to those proposed by Born and showed that the field strength of large fields differs strongly from those of small fields.
Abstract: [arXiv:physics/0605038]: According to Dirac’s theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell’s equations in the vacuum. These changes are calculated in the special case that no real electrons or positrons are present and the field varies little over a Compton wavelength. The resulting effective Lagrangian of the field reads: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) + conj.}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) - conj. } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. $\cal{E}$, $\cal{B}$ field strengths. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle 137} \frac{\displaystyle e}{\displaystyle(e^2/m c^2)^2}$ critical field strengths. The expansion terms in small fields (compared to $\cal{E}$) describe light-light scattering. The simplest term is already known from perturbation theory. For large fields, the equations derived here differ strongly from Maxwell’s equations. Our equations will be compared to those proposed by Born. Original German abstract [Z.Phys. 98(1936)714]: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert. Es ergibt sich fur das Feld eine Lagrange-Funktion: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) + konj}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) - konj } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. ($\cal{E}$, $\cal{B}$ Kraft auf das Elektron. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle ,,137``} \frac{\displaystyle e}{\displaystyle (e^2/m c^2)^2}$ „Kritische Feldstarke“.) Ihre Entwicklungsglieder fur (gegen $\vert\cal{E}_k\vert$) kleine Felder beschreiben Prozesse der Streuung von Licht an Licht, deren einfachstes bereits aus einer Storungsrechnung bekannt ist. Fur grose Felder sind die hier abgeleiteten Feldgleichungen von den Maxwellschen sehr verschieden. Sie werden mit den von Born vorgeschlagenen verglichen.
2,059 citations
TL;DR: In this article, the nuclear forces can be derived using effective chiral Lagrangians consistent with the symmetries of QCD, and the status of the calculations for two and three nucleon forces and their applications in few-nucleon systems are reviewed.
Abstract: Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.
1,455 citations
TL;DR: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums as discussed by the authors.
Abstract: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert.
1,439 citations
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01 Jan 1985TL;DR: In this article, the authors deal with phenomena that occur in the presence of strong electromagnetic fields, where the behavior of electrons (or positrons) under the influence of weak perturbations is considered.
Abstract: Up to now, our considerations in this book have mainly treated the behaviour of electrons (or positrons) under the influence of weak perturbations. In this chapter we want to deal with phenomena that occur in the presence of strong electromagnetic fields.1
882 citations
TL;DR: In this article, a unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory.
Abstract: A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a point further than that reached by these authors, in the discussion of higher order radiative reactions and vacuum polarization phenomena. However, the theory of these higher order processes is a program rather than a definitive theory, since no general proof of the convergence of these effects is attempted.The chief results obtained are (a) a demonstration of the equivalence of the Feynman and Schwinger theories, and (b) a considerable simplification of the procedure involved in applying the Schwinger theory to particular problems, the simplification being the greater the more complicated the problem.
863 citations