Summary
The emission and absorption of electromagnetic radiation is considered within the eikonal approximation in a given time-orientable background space-time. It is shown that within this approximation it is possible to interpret both advanced and retarded signals. With the further restriction that the space-time be asymptotically flat, a classical (nonquantum but strictly relativistic) particle-antiparticle distinction is introduced. This distinction is extended unambiguously to the entire space-time for timelike trajectories. The arguments are then demonstrated explicitly in the Schwarzschild space-time.
Riassunto
Si studia nell’approssimazione iconale l’emissione e l’assorbimento di radiazione elettromagnetica in un dato spazio-tempo di fondo orientabile col tempo. Si mostra che in questa approssimazione è possibile interpretare sia segnali avanzati che segnali ritardati. Con l’ulteriore restrizione che lo spazio-tempo sia asintoticamente piano, si introduce una distinzione particella-antiparticella classica (non quantistica ma strettamente relativistica). Si estende questa distinzione in modo non ambiguo all’intero spazio-tempo per traiettorie temporali. Si dimostrano poi esplicitamente le ipotesi nello spazio-tempo di Schwarzschild.
Резюме
В рамках эйконального приближения рассматриваются испускание и поглощение электромагнитного излучения в заданном фоновом пространствевремени с ориентируемым временем. Показывается, что в этом приближении возможно интерпретировать и опережающий и запаздывающий ситналы. Используя дополнительное ограничение, что пространство-время является асимптотически плоским, вводится различие между классическими (неквантовыми, но строго релятивистскими) частицей и античастицей. Это различие однозначно обобщается на полное пространство-время для времениподобных траекторий. Затем эти аргументы демонстрируются в явном виде в пространстве-времени Шварцшильда.
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References
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Lake, K., Roeder, R.C. & Honig, E. Applications of time symmetry in certain time-orientable space-times. Nuov Cim B 32, 457–476 (1976). https://doi.org/10.1007/BF02727651
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DOI: https://doi.org/10.1007/BF02727651