dorsal/arxiv
View SchemaRelativistic Quantum Transport Theory for Electrodynamics
| Authors | P. Zhuang, U. Heinz |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9502034 |
| URL | https://arxiv.org/abs/nucl-th/9502034 |
| DOI | 10.1006/aphy.1996.0011 |
| Journal | Ann.Phys.245:311-338,1996 |
Abstract
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy average we study the classical limit of the resulting three-dimensional kinetic equations. There are only two independent spinor components in this limit, the mass density and the spin density, and we derive also their covariant equations of motion. We then show that the equal-time kinetic equation provides a complete description only for constant external electromagnetic fields, but is in general incomplete. It must be supplemented by additional constraints which we derive explicitly from the covariant formulation.
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"abstract": "We investigate the relationship between the covariant and the\nthree-dimensional (equal-time) formulations of quantum kinetic theory. We show\nthat the three-dimensional approach can be obtained as the energy average of\nthe covariant formulation. We illustrate this statement in scalar and spinor\nQED. For scalar QED we derive Lorentz covariant transport and constraint\nequations directly from the Klein-Gordon equation rather than through the\npreviously used Feshbach-Villars representation. We then consider pair\nproduction in a spatially homogeneous but time-dependent electric field and\nshow that the pair density is derived much more easily via the energy averaging\nmethod than in the equal-time representation. Proceeding to spinor QED, we\nderive the covariant version of the equal-time equation derived by\nBialynicki-Birula et al. We show that it must be supplemented by another\nself-adjoint equation to obtain a complete description of the covariant spinor\nWigner operator. After spinor decomposition and energy average we study the\nclassical limit of the resulting three-dimensional kinetic equations. There are\nonly two independent spinor components in this limit, the mass density and the\nspin density, and we derive also their covariant equations of motion. We then\nshow that the equal-time kinetic equation provides a complete description only\nfor constant external electromagnetic fields, but is in general incomplete. It\nmust be supplemented by additional constraints which we derive explicitly from\nthe covariant formulation.",
"arxiv_id": "nucl-th/9502034",
"authors": [
"P. Zhuang",
"U. Heinz"
],
"categories": [
"nucl-th"
],
"doi": "10.1006/aphy.1996.0011",
"journal_ref": "Ann.Phys.245:311-338,1996",
"title": "Relativistic Quantum Transport Theory for Electrodynamics",
"url": "https://arxiv.org/abs/nucl-th/9502034"
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