Linear Modifications in the Maxwell Field Equations
TL;DR: In this article, the charge and current densities were obtained for the positron theory induced in vacuum by an electromagnetic field, accurate to the first order in ${e}^{2}$, and the corresponding correction terms in the Maxwell field equations involve integral operators.
Abstract: Expressions, accurate to the first order in ${e}^{2}$, are obtained for the charge and current densities which, according to positron theory, are induced in vacuum by an electromagnetic field. Because the corresponding correction terms in the Maxwell field equations involve integral operators, it does not seem possible to treat the modified field equations by Hamiltonian methods.
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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: 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
Book•
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
TL;DR: Theoretical energy levels and energy-level separations for n = 1 and n = 2 states of hydrogen-like atoms with nuclear charge numbers in the range 1 ⩽ Z⩽ 110 are tabulated in this paper.
501 citations