Summary
Exact solutions have been found, for a restricted class of plane-wave external fields, for the Dirac equation generalized through the addition of an anomalous magnetic moment and an electric dipole moment term. These solutions have been used to calculate the corresponding classical equations for the trajectory and the precession of polarization. In fact, we obtain the polarization directly in the integrated form and only subsequently verify its equation of motion. It is seen to obeyexactly the classical BMT equation proposed initially only for homogeneous fields and verified for nonhomogeneous fields only up to an approximation.
Riassunto
Si sono trovate soluzioni esatte, per una classe ristretta di campi esterni d’onde piane, per l’equazione di Dirac generalizzata mediante l’aggiunta di un momento magnetico anomalo e di un termine di momento di dipolo elettrico. Si sono adoperate queste soluzioni per calcolare le corrispondenti equazioni classiche per la traiettoria e la precessione della polarizzazione. In effetti si ottiene la polarizzazione direttamente nella forma integrata e solo successivamente si verifica la sua equazione di moto. Si osserva che essa ubbidisceesattamente all’equazione classica di BMT proposta inizialmente solo per campi omogenei e solo approssimativamente verificata per campi non omogenei.
Резюме
Для ограниченного класса плоско-волновых внешних полей были найдены точные решения для уравнения Дирака, обобщенного путем добавления аномального магнитного момента и члена электрического дипольного момента. Эти решения были использованы для определения соответствующих классических уравнений для траектории и прецессии поляризации. В действительности, мы полу-чаем поляризацию прямо в интегральной форме и затем только проверяем ее урав-нение движения. Показывается, что поляризациямочно подчиняется классичес-кому ВМТ уравнению, предположенному сначала только для однородных полей и проверенному для неоднороных полей только приближенно.
Similar content being viewed by others
References
D. M. Volkov:Zeits. Phys.,94, 250 (1935).
L. S. Brown andT. W. B. Kibble:Phys. Rev.,133, A 705 (1964);A. I. Nikishov andV. I. Ritus:Sov. Phys. JETP,19, 529 (1964);Žurn. Ėksp. Teor. Fiz.,46, 776 (1963));N. D. Sen Gupta:Zeits. Phys.,201, 222 (1961).P. J. Redmond:Jour. Math. Phys.,6, 1163 (1965). Many other relevant sources are quoted in the above three references.
V. Bargmann, L. Michel andV. L. Telegdi:Phys. Rev. Lett.,2, 435 (1959). (More details are given in the unpublished seminar notes ofL. Michel (1959)).
A. Chakrabarti:Nuovo Cimento,43 A, 576 (1966).
S. I. Rubinow andJ. B. Keller:Phys. Rev.,131, 2789 (1963);M. Kolsrud:Nuovo Cimento,39, 504 (1965);E. Plahte:Suppl. Nuovo Cimento,4, 246 (1966);P. Nyborg:Nuovo Cimento,31, 1209 (1964);H. Bacry:Ann. de Phys.,8, 197 (1963). Many other sources are quoted in these articles.
P. A. M. Dirac:Rev. Mod. Phys.,21, 392 (1949);34, 592 (1962).
G. N. Fleming:Journ. Math. Phys.,7, 1959 (1966).
Since τ=u·x, the relation (3.3) indicates thatu must be expressible in the form ((n·u)−1 n+σ) where σ·x=0 and the spacelike σ restoresu 2=1. The implicit forms obtained for the trajectory makes the explicit verification of the above fact rather difficult. The calculation leading to (3.3) is however very transparent, leaving no ambiguity possible.
Author information
Authors and Affiliations
Additional information
Traduzione a cura della Redazione.
Перевебено ребакцией.
Rights and permissions
About this article
Cite this article
Charkrabarti, A. Exact solution of the Dirac-Pauli equation for a class of fields: Precession of polarization. Nuovo Cimento A (1965-1970) 56, 604–624 (1968). https://doi.org/10.1007/BF02819823
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02819823