Operator quantization of non-abelian gauge theories in a completely fixed axial gauge |
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| Institution: | 1. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, School of Physics and Electronics, Hunan Normal University, Changsha, 410081, China;2. College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China;3. College of Physics, Sichuan University, Chengdu, 610064, China;4. International Collaborative Laboratory of 2D Materials for Optoelectronics Science and Technology, Engineering Technology Research Center for 2D Material Information Function Devices and Systems of Guangdong Province, Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen, 518060, China;5. Academy for Quantum Science and Technology, Zhengzhou University of Light Industry, Zhengzhou, 450002, China;1. Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA;2. SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA;3. Universidad de Costa Rica, San José, Costa Rica;1. Center for Elements Strategy Initiative for Structure Materials (ESISM), Kyoto University, Sakyo, Kyoto 606-8501, Japan;2. Department of Materials Science and Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan;3. Nanostructures Research Laboratory, Japan Fine Ceramics Center, Atsuta, Nagoya 456-8587, Japan;1. Department of Physics and Astronomy, University of Sussex, Brighton, BN1 9QH, United Kingdom;2. Department of Physics and Astronomy, Michigan State University, United States of America |
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| Abstract: | A consistent quantization of chromodynamics in a completely fixed axial gauge is carried out by using the Dirac bracket quantization procedure. The main results are: The translation of Dirac brackets into equal-time commutators is possible, without ambiguities, because of the absence of ordering problems. All equal-time commutators are compatible with constraints and gauge conditions holding as strong operator relations. All equal-time commutators are compatible with chromoelectric, chromomagnetic, and fermionic fields vanishing at spatial infinity. The colored gauge potentials A0,a, A1,a, and A2,a are seen to develop a physically significant, although pure gauge, behavior at x3 = ± ∞, as required by the presence of a nontrivial topological content. Poincaré invariance is satisfied without introducing in the Hamiltonian “extra” quantum mechanical potentials. The determinant of the Faddeev-Popov matrix does not depend upon the field variables. |
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