New Energy-Momentum And Angular Momentum Tensors And Their Applications

The internal structure of nucleon is the forefront of studies of hadron physics,but there is still no satisfying answer of the origin of nucleon spin.Within the framework of Quantum Chromodynamics(QCD),the nucleon spin can be understood as sum of the spin and orbital angular momentum of the quarks and gluons inside the nucleon.However,QCD allows different decompositions of nucleon spin,implying different structural pictures of nucleon.Essentially,the different decompositions origin from the choices of different QCD energy-momentum and angular momentum tensors.Which energymomentum and angular momentum tensor can better describe the picture of nucleon spin structure?As the conserved currents of space-time symmetry,energy-momentum and angular momentum tensors cannot be uniquely determined by the corresponding conservation laws.However,the different expressions of energy-momentum and angular momentum tensors are different regarding effectiveness.For example,in the case of the phenomenon related to the angular momentum of light,the traditional canonical expressions of energy-momentum and angular momentum tensors are more effective than the symmetrical ones.In Einstein's theory of gravitation,the symmetrical energy-momentum tensor is the effective gravitational source,while in Einstein-Cartan theory the canonical one is.How can we choose the effective expression of energy-momentum and angular momentum tensors? We propose a criterion on the energy-momentum and angular momentum tensors to restrict their forms from a special perspective of quantum measurement of mutual conserved quantities.Interestingly,this criterion expels both the conventional canonical and symmetric energy-momentum tensors and their associated angular momentum tensors.Motivated by this criterion,we derive the new energymomentum and angular momentum tensors as Noether currents from a modified Lagrangian with a second derivative.Then,we present some possible theoretical schemes to experimentally test the criterion of quantum measurement and the new energy-momentum and angular momentum tensors.We provide three possible cases in which two physical quantities are conserved at the same time and give some interesting predictions.Firstly,consider electrons in the mutual eigenstates of energy and charge.According to the collapse of the wave function in the standard quantum mechanics,we find that different energymomentum tensors show a significant difference: the symmetric energy-momentum tensor of electron field would destroy the consistency between conservations of quantum charge and energy,while both the canonical and the new energy-momentum tensors would not.Secondly,consider the joint conservations of energy and momentum.Interestingly,the traditional canonical and symmetric energymomentum tensors exhibit anomalous reverse momentum flux,while the new energy-momentum tensor does not.Thirdly,consider the multipole radiation field in a mutual eigenstate of energy and angular momentum.It can be verified that the new energy-momentum and angular momentum tensors are consistent with the criterion of quantum measurement,while the corresponding tensors of the canonical and symmetric forms are not.Next,we discusses the possible applications of the new energy-momentum and angular momentum tensors.We focuses on an interesting phenomenon,the geometric spin Hall effect(GSHE).We extend the original GSHE in several aspects,including from photon fields to the electron fields,from the energy flux to the momentum flux,from spin to orbit angular momentum,from a flat space-time to a curved space-time background,and we find the anomalous GSHE.The GSHE not only shows rich and interesting phenomena in itself,but also can be used as an effective probe to distinguish different energy-momentum tensors.What's more,the method based on the free field can also be applied to the interaction field,which can shed new light on the study of nucleon spin structures.Finally,we discuss the possible gravitational coupling of the new energy-momentum tensor and angular momentum tensors.We construct a new gravitational model in Riemann-Cartan space-time.In fact,it can be treated as an extended theory of the Einstein-Cartan theory,requesting that the generalized covariant extensions of the new energy-momentum and spin current tensors generate the spacetime curvature and space-time torsion,respectively.