بازفرمول‌بندی لاگرانژی الکتروستاتیک ماکسول بر اساس یک توسیع تک پارامتری از جبر هایزنبرگ در یک فضای فاز شش بعدی

نوع مقاله : مقاله پژوهشی کامل

نویسندگان

گروه فیزیک،دانشکده علوم پایه، دانشگاه اراک، اراک

چکیده

در یک مجموعه از مقالات (Czechoslovak Journal of Physics, 53 (2003) 1035-1040; Found. Phys, 46 (2016) 1666-1679) فریدریشاک به همراه تکاچوک یک توسیع تک پارامتری با پارامتر دگرگونش را از جبر استاندارد هایزنبرگ در یک فضای فاز شش بعدی ارائه دادند. در این مقاله، ما به بازفرمول‌بندی لاگرانژی نظریه‌ی الکتروستاتیک ماکسول در یک فضای فاز شش بعدی از منظر جبر هایزنبرگ تعمیم یافته معرفی شده توسط این نویسندگان می‌پردازیم. بعد از به دست آوردن شکل دقیق پتانسیل الکتروستاتیکی و میدان الکتریکی وابسته به یک بار نقطه‌ای ایستا در این الکتروستاتیک تعمیم یافته (الکتروستاتیک ماکسول تعمیم یافته) نشان می‌دهیم که مقدار این عبارت‌ها در مکان قرار گرفتن بار نقطه‌ای برخلاف نظریه‌‌ی ماکسول مقادیری متناهی به دست می‌آیند. نشان می‌دهیم که تمامی نتایج به دست آمده برای الکتروستاتیک ماکسول تعمیم یافته در حد انرژی‌‌‌های پایین (فواصل فضایی بزرگ) با نتایج به دست آمده از الکتروستاتیک ماکسول سازگار هستند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Lagrangian reformulation of Maxwell electrostatics based on a one-parameter extension of the Heisenberg algebra in a six-dimensional phase space

نویسندگان [English]

  • Saeed Nabipour
  • Seyed Kamran Moayedi
Department of Physics, Faculty of Basic Sciences, Arak University, Arak
چکیده [English]

In a series of papers, Frydryszak and Tkachuk (Czechoslovak Journal of Physics, 53 (2003) 1035-1040; Found. Phys, 46 (2016) 1666-1679) introduced a one-parameter extension of the Heisenberg algebra with a deformation parameter in a six-dimensional phase space. In this paper, after Lagrangian reformulation of Maxwell electrostatics from the viewpoint of the above one-parameter extension of the Heisenberg algebra in a six-dimensional phase space the electrostatic potential and the electric field of a point charge are calculated analytically in this generalized electrostatics (generalized Maxwell electrostatics). We show that in contrast with the conventional Maxwell electrostatics the electrostatic potential and the electric field of a point charge are not singular at the position of the point charge in this generalized electrostatics. We show that in the low-energy limit (large spatial distances), the results of this generalized electrostatics are compatible with the results of the conventional Maxwell electrostatics.

کلیدواژه‌ها [English]

  • Phase space
  • Heisenberg algebra
  • Deformation
  • Maxwell electrostatics
  • Lagrangian formulation
  • Point charge
 
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