We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gau...We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.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
Talcing Dirac's large number hypothesis as true, we have shown [Commun.Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory ofgeneral relativity with fixed gravitation c...Talcing Dirac's large number hypothesis as true, we have shown [Commun.Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory ofgeneral relativity with fixed gravitation constant G to cosmology, and a modified theory for varyingG is found, which reduces to Einstein's theory outside the gravitating body for phenomena of shortduration in small distances, thereby agrees with all the crucial tests formerly supportingEinstein's theory. The modified theory, when applied to the usual homogeneous cosmological model,gives rise to a variable cosmological tensor term determined by the derivatives of G, in place ofthe cosmological constant term usually introduced ad hoc. Without any free parameter thetheoretical Hubble's relation obtained from the modified theory seems not in contradiction toobservations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys.(Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004)703 we shall study in this paper the modification of electromagnetism due to Dirac's large numberhypothesis in more detail to show that the approximation of geometric optics still leads to nullgeodesies for the path of light, and that the general relation between the luminosity distance andthe proper geometric distance is still valid in our theory as in Einstein's theory, and give theequations for homogeneous cosmological model involving matter plus electromagnetic radiation.Finally we consider the impact of the modification to quantum mechanics and statistical mechanics,and arrive at a systematic theory of evolving natural constants including Planck's h as well asBoltzmann's k_B by finding out their cosmologically combined counterparts with factors ofappropriate powers of G that may remain truly constant to cosmologically long time.展开更多
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We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool toanalyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given.
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.
文摘Talcing Dirac's large number hypothesis as true, we have shown [Commun.Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory ofgeneral relativity with fixed gravitation constant G to cosmology, and a modified theory for varyingG is found, which reduces to Einstein's theory outside the gravitating body for phenomena of shortduration in small distances, thereby agrees with all the crucial tests formerly supportingEinstein's theory. The modified theory, when applied to the usual homogeneous cosmological model,gives rise to a variable cosmological tensor term determined by the derivatives of G, in place ofthe cosmological constant term usually introduced ad hoc. Without any free parameter thetheoretical Hubble's relation obtained from the modified theory seems not in contradiction toobservations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys.(Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004)703 we shall study in this paper the modification of electromagnetism due to Dirac's large numberhypothesis in more detail to show that the approximation of geometric optics still leads to nullgeodesies for the path of light, and that the general relation between the luminosity distance andthe proper geometric distance is still valid in our theory as in Einstein's theory, and give theequations for homogeneous cosmological model involving matter plus electromagnetic radiation.Finally we consider the impact of the modification to quantum mechanics and statistical mechanics,and arrive at a systematic theory of evolving natural constants including Planck's h as well asBoltzmann's k_B by finding out their cosmologically combined counterparts with factors ofappropriate powers of G that may remain truly constant to cosmologically long time.
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.
