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Title of Journal: Nuovo Cimento A 19651970

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Abbravation: Il Nuovo Cimento A (1965-1970)

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Springer Berlin Heidelberg

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DOI

10.1007/bf03043281

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1826-9869

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Reduction of complex electromagnetic fields to the

Authors: B S Rajput
Publish Date: 1970/04/01
Volume: 66, Issue: 3, Pages: 517-535
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Abstract

In the present paper we study the reduction of the wave function which transforms as electromagnetic fields to the irreducible representation of proper inhomogeneous orthochronous Lorentz group The electromagnetic fields are expanded into the modes with the amplitudes as wave functions for massless particles of spin 0 and 1 The values of electromagnetic fields in terms of these expansions are calculated as the solution of Maxwells equations in free space with and without the source In the presence of source we derive the expansions for longitudinal and transverse electric and magnetic fields and prove that in electromagnetic waves the horizontal component of the magnetic field is always zero while in the absence of source we discuss the two types of circular polarizations of electromagnetic waves by proving that only spin1 wave functions contribute to the electromagnetic fields in this case In the end we study the second quantization of the electromagnetic fields on replacing the wave function and their complex conjugates by destruction and the construction operators respectivelyВ настоящей статье мы исследуем приведение волновой функции которая преобразуется как злектромагнитные поля к неприводимому прелставлению собственной неоднородной ортохронной группы Лорентца Электромагнитные поля разлагаются по модам с некоторыми амплитудами также как волновые функции для безмассовых частиц со спином 0 и 1 Вычисляются значения электромагнитных полей в терминах этих разложений как рещение уравнений Максвелла в свободном пространстве с и без источника В присутствии источника мы выводим разложения для продольных и поперечных электрических и магнитных полей и доказываем что в электромагнитной волне горизонтальная компонента магнитного поля всегда равха нулю тогда как в отсутствии источника мы обсуждаем два типа круговых поляризаций электромагнитных волн доказывая что только волновые функции со спином единица дают вклад в электромагнитные поля в этом случае В заключение мы исследуем вторичное квантование электромагнитных полей посредством замены волновых функций и их комплексно сопряженных соответственно операторами пождемния и уничтоженияIn questo articolo si studia la riduzione della funzione donda che si trasforma come i campi elettromagnetici rispetto alla rappresentazione irriducibile del gruppo di Lorentz ortocrono non omogeneo e proprio Si sviluppano i campi elettromagnetici in modi con le ampiezze come funzioni donda per particelle prive di massa di spin 0 e 1 Si calcolano i valori dei campi elettromagnetici in termini di questi sviluppi come la soluzione delle equazioni di Maxwell nel vuoto con e senza sorgente In presenza di una sorgente si ricavano gli sviluppi per i campi magnetico ed elettrico trasversali e longitudinali e si prova che nellonda elettromagnetica la componente orizzontale del campo magnetico è sempre zero mentre in assenza di sorgente si discutomo i due tipi di polarizzazioni circolari delle onde elettromagnetiche dimostrando che in questo caso solo le funzioni donda di spin 1 contribuiscono ai campi elettromagnetici Infine si studia la seconda quantizzazione dei campi elettromagnetici sostituendo la funzione donda e i suoi complessi coniugati con gli operatori di distruzione e di creazione rispettivamente

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