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Register a new userNilpotent symmetry invariance in the superfield formulation: the (non-)Abelian 1-form gauge theories
التناسق المتغير للنيلبوتن في التنسيق الحقل السوبر: النظم الضبط الشكل الأبيلي 1-form (غير-) أبيلية
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R. P. Malik
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نحن نلتقط التناسق الصامت الصفري Becchi-Rouet-Stora-Tyutin (BRST) والمضاد له على الطرفين غير المشغول والمشغول من تراكيب الغارقة للنظريات الغارقة الأبعاد (3 + 1) (غير-)أبيلية 1-form في إطار الصيغة السوبر المحددة. وبالأخص، نوفر التفسيرات الهندسية لـ (i) التناسق الصامت الصفري أعلاه، و (ii) تراكيب الغارقة أعلاه، في لغة الكميات المحددة في مجال الصيغة السوبر المذكورة أعلاه. وتتضح بعض النقاط الحساسة المتعلقة بنظريات الغارقة الأبعاد (غير-)أبيلية 1-form في إطار الصيغة السوبر المذكورة حيث تناقش نظريات الغارقة العادية الأبعاد 4 في المتضخم السوبر (4، 2) الذي يتم تعريفه بواسطة أربعة إحداثيات الفضاء الزمني x^mu (بمعنى mu = 0، 1، 2، 3) وزوج من المتغيرات الغراسمية theta وbartheta. وتعد أحد أبرز نتائج دراستنا الحالية بسهولة كبيرة في الفهم الهندسي للتناسق الصامت الصفري (المضاد له).
We capture the off-shell as well as the on-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four spacetime coordinates x^mu (with mu = 0, 1, 2, 3) and a pair of Grassmannian variables theta and bartheta. One of the key results of our present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry invariance.
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