اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدنظرية الحقل الكمي لاكرانجي في الصورة الحذفية. IV. العلاقات التراكمية للحقول الحرة
Lagrangian quantum field theory in momentum picture. IV. Commutation relations for free fields
87
0
0.0
(
0
)
اسأل ChatGPT حول البحث
تُناقش من وجهة نظر رياضية علاقات التبادل الجبرية المحتملة في نظرية لاقونية الكم الحر للحقول المقياسية والإشارية والمتجهة. كمصادر لهذه العلاقات تستخدم المعادلات/العلاقات الهايزنبرج للمتغيرات الديناميكية وشرط محدد للفردية لمشغلات المتغيرات الديناميكية (مقابل بعض الطبقات من اللاقونيات). وتشير العلاقات الجانبية التبادلية أو بعض تطويراتها إلى أنها الأكثر عامة والتي تؤدي إلى صحة كل معادلات هايزنبرج. يصبح الامتثال لمعادلات هايزنبرج وشرط الفردية أمراً مستحيلاً. ويتم حل هذه المشكلة من خلال إعادة تعريف المتغيرات الديناميكية، مماثلة لعملية الترتيب الطبيعي والتي تشملها كحالة خاصة. وهذا يؤدي إلى تغييرات مقبولة في العلاقات التبادلية. وتضيف دخول مفهوم الفراغ إلى الطبقة المحتملة للعلاقات التبادلية؛ وبالخصوص، يقتضي ذلك تخفيض إعادة تعريف المتغيرات الديناميكية إلى الترتيب الطبيعي. ويتم تطبيق آخر قيد على هذه الطبقة من خلال الطلب عن وجود إجراء تحليلي فعال لحساب القيم المتوسط للفراغ. وتشير العلاقات التبادلية المثلثية القياسية إلى الوحيدة المعروفة التي تلبي كل من الشروط المذكورة ولا تتناقض مع البيانات الحالية.
Possible (algebraic) commutation relations in the Lagrangian quantum theory of free (scalar, spinor and vector) fields are considered from mathematical view-point. As sources of these relations are employed the Heisenberg equations/relations for the dynamical variables and a specific condition for uniqueness of the operators of the dynamical variables (with respect to some class of Lagrangians). The paracommutation relations or some their generalizations are pointed as the most general ones that entail the validity of all Heisenberg equations. The simultaneous fulfillment of the Heisenberg equations and the uniqueness requirement turn to be impossible. This problem is solved via a redefinition of the dynamical variables, similar to the normal ordering procedure and containing it as a special case. That implies corresponding changes in the admissible commutation relations. The introduction of the concept of the vacuum makes narrow the class of the possible commutation relations; in particular, the mentioned redefinition of the dynamical variables is reduced to normal ordering. As a last restriction on that class is imposed the requirement for existing of an effective procedure for calculating vacuum mean values. The standard bilinear commutation relations are pointed as the only known ones that satisfy all of the mentioned conditions and do not contradict to the existing data.
قيم البحث
اقرأ أيضاً
We discuss the renormalisation of the initial value problem in quantum field theory using the two-particle irreducible (2PI) effective action formalism. The nonequilibrium dynamics is renormalised by counterterms determined in equilibrium. We emphasi
ze the importance of the appropriate choice of initial conditions and go beyond the Gaussian initial density operator by defining self-consistent initial conditions. We study the corresponding time evolution and present a numerical example which supports the existence of a continuum limit for this type of initial conditions.
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations <V_2|V_1> and <V_3|V_1> in the NS fermionic strin
g field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
The Elko quantum field was introduced by Ahluwalia and Grumiller, who proposed it as a candidate for dark matter. We study the Elko field in Weinbergs formalism for quantum field theory. We prove that if one takes the symmetry group to be the full Po
incare group then the Elko field is not a quantum field in the sense of Weinberg. This confirms results of Ahluwalia, Lee and Schritt, who showed using a different approach that the Elko field does not transform covariantly under rotations and hence has a preferred axis.
By the use of cyclic symmetry, KK relations and BCJ relations, one can reduce the number of independent $N$-point color-ordered tree amplitudes in gauge theory and string theory from $N!$ to $(N-3)!$. In this paper, we investigate these relations at
tree-level in both string theory and field theory. We will show that there are two primary relations. All other relations can be generated by the primary relations. In string theory, the primary relations can be chosen as cyclic symmetry as well as either the fundamental KK relation or the fundamental BCJ relation. In field theory, the primary relations can only be chosen as cyclic symmetry and the fundamental BCJ relation. We will further show a kind of more general relation which can also be generated by the primary relations. The general formula of the explicit minimal-basis expansions for color-ordered open string tree amplitudes will be given and proven in this paper.
We present two different aspects of the anomalies in quantum field theory. One is the dispersion relation aspect, the other is differential geometry where we derive the Stora--Zumino chain of descent equations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
