Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework...In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.展开更多
The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identi...The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identities,it can be shown that the constraint multipliers connected with the first-class constraints may not be independent, so a query to a conjecture of Dirac is presented. Based on the symmetry properties of the constrained Hamiltonian system in phase space, a counterexample to a conjecture of Dirac is given to show that Dirac's conjecture fails in such a system.We present here a different way rather than Cawley's examples and other's ones in that there is no linearization of constraints in the problem. This example has a feature that neither the primary first-class constraints nor secondary first-class constraints are generators of the gauge transformation.展开更多
By using the Faddeev Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics （QED）. In the sense of Dirac＇s conjecture, we deduce all the constraints and give Di...By using the Faddeev Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics （QED）. In the sense of Dirac＇s conjecture, we deduce all the constraints and give Dirac＇s gauge transformations （DGT）. According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for tile composite fermions in QBD. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Purthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional （x, y） plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential.展开更多
文摘Dirac's method which itself is for constrained Boson fields and particle systems is followed and developed to treat Dirac fields in light-front coordinates.
文摘In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.
文摘The extended canonical Noether identities and canonical first Noether theorem derived from an extended action in phase space for a system with a singular Lagrangian are formulated. Using these canonical Noether identities,it can be shown that the constraint multipliers connected with the first-class constraints may not be independent, so a query to a conjecture of Dirac is presented. Based on the symmetry properties of the constrained Hamiltonian system in phase space, a counterexample to a conjecture of Dirac is given to show that Dirac's conjecture fails in such a system.We present here a different way rather than Cawley's examples and other's ones in that there is no linearization of constraints in the problem. This example has a feature that neither the primary first-class constraints nor secondary first-class constraints are generators of the gauge transformation.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11047020 and 11047173)the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2011AM019, ZR2010AQ025, BS2010DS006, and Y200814)the Scientific and Technological Development Project of Shandong Province, China (Grant No. J08LI56)
文摘By using the Faddeev Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics （QED）. In the sense of Dirac＇s conjecture, we deduce all the constraints and give Dirac＇s gauge transformations （DGT）. According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for tile composite fermions in QBD. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Purthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional （x, y） plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential.
