Folgerungen aus der Diracschen Theorie des Positrons

Heisenberg, W.; Euler, H.

doi:10.1007/bf01343663

Cited by 2,770 publications

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“…This action can be regarded as a non-local version of the well-known Euler-Heisenberg Lagrangian [22]. Clearly, ln(−∇ 2 /µ 2 ) corresponds to ln(p 2 /µ 2 ) contribution in momentum space, therefore, the electric charge 'runs' as the momentum changes.…”

Section: Discussionmentioning

confidence: 99%

Renormalization group and decoupling in curved space

Gorbar

2004

Nuclear Physics B - Proceedings Supplements

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It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for important cosmological applications like the graceful exit from the inflation and low-energy quantum dynamics of the cosmological constant. We investigate, using both covariant and non-covariant methods of calculations and mass-dependent renormalization scheme, the vacuum quantum effects of a massive scalar field in curved space-time. In the higher derivative sector we arrive at the explicit form of decoupling and obtain the β-functions in both UV and IR regimes as the limits of general expressions. For the cosmological and Newton constants the corresponding β-functions are not accessible in the perturbative regime and in particular the form of decoupling remains unclear.

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Section: Discussionmentioning

confidence: 99%

Renormalization group and decoupling in curved space

Gorbar

2004

Nuclear Physics B - Proceedings Supplements

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“…Since Heisenberg and Euler [23] noted that quantum electrodynamics predicts that the electromagnetic field behaves nonlinearly through the presence of virtual charged particles, the nonlinear electrodynamics has been an interesting subject for many years [24][25][26][27][28][29][30][31][32] because the nonlinear electrodynamics carries more information than the Maxwell field. One of the important nonlinear electrodynamics is the logarithmic electromagnetic field which appears in the description of vacuum polarization effects.…”

Section: Introductionmentioning

confidence: 99%

“…One of the important nonlinear electrodynamics is the logarithmic electromagnetic field which appears in the description of vacuum polarization effects. The logarithmic terms were obtained as exact 1-loop corrections for electrons in a uniform electromagnetic field background by Euler and Heisenberg [23]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Holographic superconductor/insulator transition with logarithmic electromagnetic field in Gauss–Bonnet gravity

2012

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The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field b makes it easier for the scalar hair to be condensated;ii) the ratio of the gap frequency in conductivity ω g to the critical temperature T c depends on both b and the Gauss-Bonnet constant α; and iii) the critical exponents are independent of the b and α. For the EinsteinGauss-Bonnet AdS Soliton, we show that the system is the insulator phase when the chemical potential µ is small, but there is a phase transition and the AdS soliton reaches the superconductor (or superfluid) phase when µ larger than critical chemical potential. A special property should be noted is that the critical chemical potential is not changed by the coupling parameter b but depends on α.

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“…On the other hand, Heisenberg and Euler [3] showed in 1936 that the vacuum state of a charged quantum field interacting with a static electric field is unstable and decays into pairs. In 1951 Schwinger [4]gave the expression of this decay rate, using the technique known today as the Schwinger proper time representation of the functional integral.…”

Section: Introductionmentioning

confidence: 99%

Quantum Charged Fields in (1+1) Rindler Space

Gabriel

Spindel

2000

Annals of Physics

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We study, using Rindler coordinates, the quantization of a charged scalar field interacting with a constant (Poincaré invariant), external, electric field in (1+1) dimensionnal flatspace: our main motivation is pedagogy. We illustrate in this framework the equivalence between various approaches to field quantization commonly used in the framework of curved backgrounds. First we establish the expression of the Schwinger vacuum decay rate, using the operator formalism. Then we rederive it in the framework of the Feynman path integral method. Our analysis reinforces the conjecture which identifies the zero winding sector of the Minkowski propagator with the Rindler propagator. Moreover we compute the expression of the Unruh's modes that allow to make connection between Minkowskian and Rindlerian quantization scheme by purely algebraic relations. We use these modes to study the physics of a charged two level detector moving in an electric field whose transitions are due to the exchange of charged quanta. In the limit where the Schwinger pair production mechanism of the exchanged quanta becomes negligible we recover the Boltzman equilibrium ratio for the population of the levels of the detector. Finally we explicitly show how the detector can be taken as the large mass and charge limit of an interacting fields system.

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Folgerungen aus der Diracschen Theorie des Positrons

Cited by 2,770 publications

References 0 publications

Renormalization group and decoupling in curved space

Renormalization group and decoupling in curved space

Holographic superconductor/insulator transition with logarithmic electromagnetic field in Gauss–Bonnet gravity

Quantum Charged Fields in (1+1) Rindler Space

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