Quaternion Octonion Reformulation of Quantum Chromodynamics

We have made an attempt to develop the quaternionic formulation of Yang–Mill’s field equations and octonion reformulation of quantum chromo dynamics (QCD). Starting with the Lagrangian density, we have discussed the field equations of SU(2) and SU(3) gauge fields for both cases of global and local gauge symmetries. It has been shown that the three quaternion units explain the structure of Yang–Mill’s field while the seven octonion units provide the consistent structure of SU(3) _C gauge symmetry of quantum chromo dynamics.     

量子色动力学与核物理

概述了量子色动力学和中高能核物理在核散射、核子特性及核子－核子相互作用势方面的密切联系． The close relation between quantum chromodynamics (QCD) and the nuclear.physics in medium and high energy regions is briefly reviewed in some aspects such as nuclear scatterings, nueleon propertics as well as the interactions between nucleons.     

Condensate Structure of the Vacuum of Quantum Chromodynamics

The non-perturbative vacuum structure of quantum chromodynamies (QCD) is studied with the help of methods which are generalizations of those used to describe condensation effects and quasi-particles in superfluid and superconductive mediums. The gluon condensation is explained by the introduction of a new vacuum state defined by a Bogoljubov transformation, leading to non-vanishing vacuum expectation values as e.g. the gluon condensation parameter, a negative vacuum energy density, and to a gap in the energy spectrum which is connected with excited quasi-particle states with a rest mass.     

Introduction of Anomalous Green Functions into Quantum Chromodynamics

The nonperturbative vacuum structure of Quantum Chromodynamic is studied with the help of a generalization of the formalism of Green functions which corresponds to the method of Gorkov and Nambu in the theory of superconductivity. Taking into account the existence of gluon condensation the selfenergy of the gluon-quasi-particles is calculated with the help of modified rules for Feynman diagrams. The resulting integral equations for the effective field parameters contain particular solutions with an energy gap in the spectrum of the quasi-particles and a phase transition at a critical momentum.     

Temperature Dependence of the CPN-1 Model and the Analogy with Quantum Chromodynamics

The two-dimensional CP^N-1 model — a simple field-theoretic analogue of four-dimensional quantum chromodynamics (QCD) — is analysed and reviewed. The major themes are the temperature dependence of the CP^N-1 model, and the analogy between CP^N-1 and QCD. A detailed treatment of the 1/N approximation of the CP^N-1 model is given. The main results emerging from this approximation are discussed at length. These are: asymptotic freedom, dimensional transmutation, confinement and topological charge nonquantization at zero temperature T = O, screening and topological charge quantization at finite temperature T. The analogy with QCD is explained in detail. A new, qualitative, analysis of the CP^N-1 model at finite temperature is introduced. This approach exploits the conformal invariance of the model to “heat” an arbitrary CP^N-1 field from T = O to finite temperature. This is achieved by conformal-transforming the flat Euclidean space-time of the T = O theory to the cylindrical space-time of the finite temperature theory.     

Quantum Chromodynamics in 1+3 Dimensions at High Temperature: Dimensional Reduction Revisited

The gluon sector of QCD in 1+3 dimensions in analyzed at high temperature (much larger than the critical ones) thereby generalizing previous results by other authors. The imaginary time formalism is used. The analysis is carried out to all orders in an improved perturbation theory which includes all second-order internal quark loops in the “free” gluon propagators. General results are given for the leading high temperature contributions to all renormalized connected gluon Green's functions (for fixed external threemomenta, much smaller than the temperature). The latter are generated by a new (dimensionally reduced) high-temperature partition function Z_HT, which corresponds to: i) the Yang-Mills (“magnetic”) gluon field coupled to a massive scalar (“electric”) gluon field, all in 3 spatial dimensions and at zero imaginary time, ii) the quark field, which continues to depend on imaginary time, coupled to the above gluon fields Z_HT also depends on the renormalized quark masses and gauge coupling constant at zero temperature, the second order quark-loop contributions to the zero-temperature renormalization constants for the gluon field and the three and four gluon vertices and on new gluon mass terms. The latter correspond to a finite number of diagrams in the improved perturbation theory at high temperature. Z_HT could be useful as the starting point for further non-perturbative studies. For the pure Yang-Mills plus ghosts theory (no quarks), it is conjectured that contributions to Green's functions depending on external momenta due to internal electric gluons could be regarded, as subdominant. Arguments are given in order to justify that conjecture. Then, the above Z_HT can be simplified and another high-temperature generating functional depending only on magnetic gluon fields is given. For the full theory including quarks, the possibility of neglecting contributions due to internal quark loops is discussed: certain infrared divergences beyond the oneloop level appear to imply that such a simplification, although not discarded, is rather hard to establish.     

Generalized Octonion Electrodynamics

We have made an attempt to reformulate the generalized field equation of dyons in terms of octonion variables. Octonion forms of generalized potential and current equations are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion electrodynamics in manifestly covariant and consistent manner.     

Transition Temperature of Lattice Quantum Chromodynamics with Two Flavors with a Small Chemical Potential

We present the results for the transition temperature of quantum chromodynamics with two degenerate flavors （Nf=2） of Wilson quarks as a function of a small baryon chemical potential μB from Monte Carlo simulations at κ=0.175, κ is the hopping parameter. By using the imaginary chemical potential for which the fermion determinant is positive and the Ferrenberg-Swendsen reweighting method, we perform simulations on lattice 83×4 with 4 being the temporal extent. By analytic continuation of the data to the real chemical potential μ, we obtain the transition temperature for the small chemical potential, and compare our results with others.     

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G_M(Q²)/Q_E(Q²) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q² behaviour of the Dirac form factor [1] is also discussed.     

Octonion massive electrodynamics

In this paper, we have made an attempt to reformulate the generalized field equation and various quantum equations of massive dyons in terms of octonion eight dimensional space as the combination of two (external and internal) four dimensional spaces. The octonion forms of generalized potential and current equations of massive dyons are discussed in consistent manner. It has been shown that due to the non associativity of octonion variables it is necessary to impose certain constraints to describe generalized octonion massive electrodynamics in manifestly covariant and consistent manner.     

The Strong Interaction in Chromodynamics

L static classical solution of nonlinear gluon field belonging to the SU(3) octet representation is obtained which is inversely proportional to the couplicg constant g, and therefore cannot be obtained by usual perturbation method. The static field is used as the potential of the relativistic wave equation of quarks in hadron states. It is found that the motion of quarks and antiquarks in all kinds of hadrons including new particles Ψ, and γ can be described by simple harmonic oscillations with small corrections due to spin-dependen t interactions.     

Reggeon, Pomeron and Glueball, Odderon-Hadron-Hadron Interaction at High Energies - From Regge Theory to Quantum Chromodynamics

Based on analysis of scattering matrix S, and its properties such as analyticity, unitarity, Lorentz invariance, and crossing symmetry relation, the Regge theory was proposed to describe hadron-hadron scattering at high energies before the advent of QCD, and correspondingly a Reggeon concept was born as a mediator of strongly interaction. This theory serves as a successful approach and has explained a great number of experimental data successfully, which proves that the Regge theory can be regarded as a basic theory of hadron interaction at high energies and its validity in many applications. However, as new experimental data come out, we have some difficulties in explaining the data. The new experimental total cross section violates the predictions of Regge theory, which shows that Regge formalism is limited in its applications to high energy data. To understand new experimental measurements, a new exchange theory was consequently born and its mediator is called Pomeron, which has vacuum quantum numbers. The new theory named as Pomeron exchange theory which reproduces the new experimental data of diffractive processes successfully. There are two exchange mediators： Reggeon and Pomeron. Reggeon exchange theory can only produce data at the relatively lower energy region, while Pomeron exchange theory fits the data only at higher-energy region, separately. In order to explain the data in the whole energy region, we propose a Reggeon-Pomeron model to describe high-energy hadron- hadron scattering and other diffractive processes. Although the Reggeon-Pomeron model is successful in describing high-energy hadron-hadron interaction in the whole energy region, it is a phenomenological model. After the advent of QCD, people try to reveal the mystery of the phenomenological theory from QCD since hadron-hadron processes is a strong interaction, which is believed to be described by QCD. According to this point of view, we study the QCD nature of Reggeon and Pomeron. We claim that the Reggeon exchange is an exchange of mult     

Octonion X,Y-productG 2 variants

The automorphism group G ₂ of the octonions changes when octonion X, Y -product variants are used. I present here a general solution for how to go from G ₂ to its X, Y -product variant.Happy birthday to Larry Horwitz. If there's a next time, you must come.     

Unified Split Octonion Formulation of Dyons

Demonstrating the split octonion formalism for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), relevant field equations are derived in compact, simpler and manifestly covariant forms. It has been shown that this unified model reproduces the dynamics of structure of fields associated with individual charges (masses) in the absence of others.     

Hyperbolic Octonion Formulation of Gravitational Field Equations

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.     

Quaternion Octonion Reformulation of Grand Unified Theories

In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann λ matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5) gauge group. We have thus described the SU(5) gauge group and its subgroup SU(3) _C ×SU(2) _L ×U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.