Wave operators for the massive charged linear Dirac field on the Reissner-Nordström metric

2000 ◽  
Vol 17 (11) ◽  
pp. 2281-2296 ◽  
Author(s):  
Fabrice Melnyk
Keyword(s):  
Dirac Field ◽  
Wave Operators

scholarly journals Infrared Problem vs Gauge Choice: Scattering of Classical Dirac Field

2021 ◽  
Author(s):  
Andrzej Herdegen
Keyword(s):  
Free Field ◽  
Asymptotic Completeness ◽  
Dirac Field ◽  
Free Evolution ◽  
Wave Operators ◽  
Radiation Fields ◽  
Scattering Wave ◽  
Long Time ◽  
Free Fields ◽  
External Time

AbstractWe consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm{ret}/\mathrm{adv}}$$ F ret / adv has past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm{in}/\mathrm{out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show the existence of the electromagnetic gauges in which the particle has ‘in’ and ‘out’ asymptotic states approaching free field states, with no long-time corrections of the free dynamics. Using a special Cauchy foliation of the spacetime, we show in this context the existence and asymptotic completeness of the wave operators. Moreover, we define a special ‘evolution picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ ; thus the scattering wave operators do not need the free evolution counteraction.

Functional Quantum Theory of Free Relativistic Fermi Fields

1970 ◽  
Vol 25 (5) ◽  
pp. 575-586
Author(s):  
H. Stumpf
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Physical Interpretation ◽  
Functional Equations ◽  
Dirac Field ◽  
Functional Hilbert Space ◽  
Free Fermi ◽  
Special Case ◽  
Relativistic Fermi

Functional quantum theory of free Fermi fields is treated for the special case of a free Dirac field. All other cases run on the same pattern. Starting with the Schwinger functionals of the free Dirac field, functional equations and corresponding many particle functionals can be derived. To establish a functional quantum theory, a physical interpretation of the functionals is required. It is provided by a mapping of the physical Hilbert space into an appropriate functional Hilbert space, which is introduced here. Mathematical details, especially the problems connected with anticommuting functional sources are treated in the appendices.

Vacuum polarization and particle creation in the presence of a potential step

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641031 ◽  
Author(s):  
S. P. Gavrilov ◽  
D. M. Gitman
Keyword(s):  
Electric Potential ◽  
Canonical Quantization ◽  
Particle Creation ◽  
Pair Creation ◽  
Dirac Field ◽  
Potential Step ◽  
Electron Positron ◽  
Physical Impact ◽  
Particle Interpretation ◽  
Electron Positron Pair

We consider QED with strong external backgrounds that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x-electric potential steps for charged particles. They can create particles from the vacuum, the Klein paradox being closely related to this process. We describe a canonical quantization of the Dirac field with x-electric potential step in terms of adequate in- and out-creation and annihilation operators that allow one to have consistent particle interpretation of the physical system under consideration and develop a nonperturbative (in the external field) technics to calculate scattering, reflection, and electron-positron pair creation. We resume the physical impact of this development.

Green function formulation of the Dirac field in curved space

1966 ◽  
Vol 294 (1439) ◽  
pp. 437-448 ◽  
Keyword(s):  
Green Function ◽  
Dirac Field ◽  
Green Functions ◽  
Field Equations ◽  
Curved Space ◽  
Particle Field ◽  
Function Formulation ◽  
Essential Idea ◽  
Mass Field

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

Remarks on the electromagnetic decays of the neutral pion

2021 ◽  
pp. 2150123
Author(s):  
Stanley A. Bruce
Keyword(s):  
Chiral Symmetry ◽  
Neutral Pion ◽  
Classical Electrodynamics ◽  
Dirac Field ◽  
Electromagnetic Decays

We propose a simple classical electrodynamics model in which a Lorentz pseudoscalar field and a Dirac field are present in the general Lagrangian of the system. The model is constructed by allowing explicit violation of chiral symmetry. This approach is intended to predict possible electromagnetic decays of the neutral pion in effective terms.

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