Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator [Formula: see text] of the parton fields is a function [Formula: see text] of Lorentz invariants [Formula: see text], the Ioffe time, and the invariant interval [Formula: see text]. This observation allows to extract the Ioffe-time distribution [Formula: see text] from Euclidean separations [Formula: see text] accessible on the lattice. Another basic feature is the use of the ratio [Formula: see text], that allows to eliminate artificial ultraviolet divergence generated by the gauge link for spacelike intervals. The remaining [Formula: see text]-dependence of the reduced Ioffe-time distribution [Formula: see text] corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions [Formula: see text] using matching relations. The [Formula: see text]-dependence of [Formula: see text] governs the [Formula: see text]-dependence of parton densities [Formula: see text]. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

Planck Gravitation Theory

The author proposes a new gravitation theory, the Planck gravitation theory. The theoretical name is in honor of Planck proposing the Planck Length. Gravitation is a force in 4-dimensional space, or a force in 5-dimensional space-time. Every quantum particle produces gravitation. Gravitation is not actually related to the mass of particles. Every quantum particle produces the same gravitation, regardless of the type of particle. The origin of gravitation is quantum, and gravitation is a quantum force. In 4-dimensional space, gravitation is inversely proportional to the cubic of distance, not square of distance. The strength of gravitation is entirely determined by the Planck Length. The Planck Length is the identification constant of gravitation. The author's earlier projection gravitation theory is only a derivation of the Planck gravitation theory. From the theory, we deduce the gravitation of photons. Planck gravitation is separated into two different patterns in 3-simensional space. For particles with rest mass, Planck gravitation translates into projection gravitation, which is inversely proportional to the square of distance. For particles with zero rest mass, gravitation is inversely proportional to the cubic of distance. Every quantum particle is an empty hole in space, the radius of empty hole is Planck Length. This brings the effect of the quantization of space-time. Planck gravitation theory can solve the problem of ultraviolet divergence in quantum field theory without the need for renormalization. If the Planck gravitation theory is true, human need to rethink the gravitation, and need to rethink the way of gravitation quantization. The author finally discusses the projection action, it is the key to human understanding of the truth about gravitation.

Quantum field formalism for the higher-derivative nonrelativistic electrodynamics in 1+1 dimensions

Starting from the classical nonrelativistic electrodynamics in 1[Formula: see text]+[Formula: see text]1 dimensions, a higher-derivative version is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of the original electrodynamics, preserving its gauge invariance. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization for the higher-derivative model is developed. By extending the Faddeev–Senjanovic algorithm, the path integral quantization is carried out. Hence, the Feynman rules are established and the diagrammatic structure is analyzed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams of the original model, where the electromagnetic field propagator is present. A generalization of the BRST quantization is also considered.

Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations

The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.

QUANTUM STRUCTURE OF FIELD THEORY AND STANDARD MODEL BASED ON INFINITY-FREE LOOP REGULARIZATION/RENORMALIZATION

To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space–time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet-divergence-preserving (UVDP) parametrization naturally leads to Bjorken–Drell's analogy between Feynman diagrams and electric circuits, which enables us to treat systematically the divergences of Feynman diagrams and understand better the divergence structure of QFTs. The LORE method has been shown to be applicable to both underlying and effective QFTs. Its consistency and advantages have been demonstrated in a series of applications, which includes the Slavnov–Taylor–Ward–Takahaski identities of gauge theories and supersymmetric theories, quantum chiral anomaly, renormalization of scalar interaction and power-law running of scalar mass, quantum gravitational effects and asymptotic free power-law running of gauge couplings.