SPACE-TIME PROPERTY OF FERMION NUMBER

Enlarging the dimensionality of Minkowski space from 4 to 5,and relating the restmass of particle with x₅ as m=—i（∂/（∂x_5）））we discuss the 5-dimensional non-linear con-formal group C（M₅）under which dx₁²+dx₂²+dx₃²-dx₀²+dx₅²=0 is invariant.The C（M₅）group is isomorphic to the linear group SO（5,2）from which we study thespace-time property of Fermion number,and the relations between half-integral（in-tegral）spin and odd（even）Fermion number are obtained.     

THE U1 GAUGE FIELD IN A SUN GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x） （λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_vλ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.     

FINE STRUCTURES OF INCLUSIVE SPECTRA(Ⅰ)——SUM RULES AND THE GENERALIZATION OF FEYNMAN-YANG SCALING

Important implications of the fine structure of inclusive spectra(to be calledinclusive and semi-inclusive spectra of nearby particles,which represent the local dis-tributions of nearby particles in three-dimensional phase space with rapidity y and transverse momenta P_⊥x, P_⊥z as independent coordinates are explained,and some basicfeatures of the fine stucture are found,namely,sum rules and the generalized formof the Feynman-Yang scaling.One of the sum rules,for example,is:where f_(1;k) denotes the normalized invariant inclusive cross section of k closely neigh-boring particles.It follows that the inclusive the spectra of nearby particles arequalitatively different from the usual ones.The generalized form of the Feynman-Yang scaling for the case of k closelyneighboring particles,for example,is:f_(1;k)(s,x₁,P_⊥1,…x_k,P_⊥k⁾∞,（s→∞,x₁≤x₂≤…≤x_k）.where‘∞’denotes‘approaches a definite limit’.For k=2,the existing experimentaldata for the rapidity gap-length distributions show that for FNAL energies,f_(1,k） isalready close to its limiting form.The inclusive（semi-inclusive）spectra of nearbyparticles way be able to reflect effectively short-range correlation effects.     

STRONG INTERACTION AND CHIRAL GAUGE FIELD

The concept of e^{iα（x）γ_s} local gauge transformation is introduced in this article. The chiral gauge invariant Lagrangian is given. The relationship between chiral gauge field and strong interaction is also discussed. In a special condition, we obtain the effective Lagrangian for V-A type strong interaction.     

CANONICAL QUANTIZATION OF GAUGE FIELDS(Ⅱ)——SPONTANEOUSLY BROKEN GAUGE FIELDS

In R_ξ gauges a SU（2）spontaneonly broken gauge theory is qnantized within the canonical formalism,and the gauge compensating term is derived.     

THE INFLUENCE OF THE SELF-ENERGY DIAGRAMS ON THE SOLUTIONS OF A SCALAR BETHE SALPETER EQUATION

The influence of the self-energy diagrams on the solutions of the Bethe-Salpe-ter equation is studied by taking a gφ₁*（x）φ₁（x）φ₂（x） interaction and under the ladder approximation. The results show for ground state solution, the self-energy diagrams will diminish the eigenvalues and alter the wave funetions slight-ly. While for the excited states and anti-symmetric solutions, the influence of theself-energy diagrams is considerable. which completely alters the properties of the solutions. The results also show that the solutions from the ladder approximationare meaningful only in the loosly bounded cases, and as the binding becomes tight,the contribution from the self-energy diagrams becomes important.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_±1/2,V±1/2）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅱ) THE NONHERMITIAN CHOICE

The cancellation properties of the nonhermitian single-particle （SP） potential u_αβ=M_αβ （ε_β） [or M_αβ（ε_α）] according to the principle of maximal cancellation of perturbation diagrams are investigated in detail. The mass operator M_αβ（ω） is separated into two parts M_αβ^on （ω） and M_αβ^off （ω） as usual, however, a new criterion for their definition will be proposed. It is shown that the exact mass operator insertion is equal to the sum of the following three types of terms:（1） terms contributed by the poles of M_αβ^off（ω）. They are truly non-factorizable and must be considered separately,（2） terms which can be cancelled to all orders by the nonhermitian choice u_αβ=M_αβ （ε_β） [or M_αβ（ε_α）]. Hence, they serve to define u_αβ,（3） the remaining terms, which can be summed to all orders in a simple way and may be interpreted as amplitude renormalization of the SP Green function.In order to illustrate the usefulness of the above results, we have considered the renormalized random phase approximation （RRPA） for the particle-hole Green function as an example. Related formulae are derived. In RRPA, not only the SP propagator renormalization which includes all the effects except those contributed by the poles of M_αβ^off （ω）, but also the off energy shell property of the G matrix elements have been taken into account.     

A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SUn GROUP

It is proved that under the Gelfand-Biedenharn phase convention any SU_n singletfactor （SF） belongs to the type of the derivable or underivable,designated as （SU_nSF）d and （SU_r SF） respectively,and （SU_n SF）d=（SU_r SF）,n=r+1,r+2,….Therefore the calculation of any SU_n Clebsch-Gordan coefficients is reduced to thecalculation of a few underivable singlet factor （SU_r SF）.     

ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SUn BARYON AND MESON WAVE FUNCTIONS

The baryon and meson wave functions of SU_n symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU₃.     

AN ANALYSIS OF FOUR-ELEMENT MODELS OF LEPTONS AND NON-DIAGONAL NEUTRAL CURRENTS

Due to the possible production of neutral and charge heavy leptons by v_μ, models consisting of four elements per "line", e.g. v_e, e^-, E⁰, E^- v_μ, μ^-, M^0, M^- v_τ, τ^-, T⁰, T^- ……are analysed. Non-diagonal neutral currents cannot be avoided. Nevertheless, a model is proposed within SU_（2）×U_（1） in which the process μ→eγ can still be suppressed by the Bjorken-Lane-Weinberg mechanism; various production cross-sections for heavy leptons are reasonable when compared with experiments. Models corresponding to SU_（3）×U（1） and still higher symmetries are discussed.     

CANONICAL QUANTIZATION OF GAUGE FIELDS (Ⅲ)——GRAVITATIONAL FIELD

The gravitational field is quantized within the canonical formalism under theharmonic gauge condition.The gravitational field is decomposed into transversalfields and self-commuting fields.The equation of motion of the self-commuting field X_μ is derived,and the contributions of self-commuting fields to physical S-matrixelements are investigated.Then the gauge compensating term of the effective actionis obtained.The result is in agreement with that obtained by the path integral method,but with our method the difficulty of the Gribov gauge ambiguity can be overcome.     

APPROXIMATE SEQUENCE FOR U（t,t0）-OPERATOR

We give an approximate sequence for U（t,t₀）-operator.We prove the follow-ing theorems:Theorem 1.If the norm ||H（t）|| of H（t）in equation（2.1）is a Lebesgue in-tegrable function with respect to t,then there is an approximate sequence{U_n},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U_1^|Ψ><Φ|U_2^|Ψ>,......,<Φ|U_n^|Ψ>,......is uniform convergent with respect to t.Theorem 2.If in finite time interval,the norm ||H（t）|| of H（t）in equation （2.1）is a Lebesgue integrable function,then equation（2.1）has unique solution.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβ（εβ）

In this paper the following results are proved:although the single-particle（sp）potential u_αβ=M_αβ（ε_β）defined in terms of the mass operator M_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=ε_γ|γ> are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] where E₀（N）denotes the exact ground state energy of a closed-shell nucleus N,and E_nγ（N±1）are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.     

QCD PREDICTION FOR THE REACTION γ+p→2γ+X

In the framework of the perturbative QCD, the two-fold differential cross section d²σ/dx_Tdx_L of the reaction γ+p→2γ+X and its two backgrounds (γ+p→γ++X, γ+p→γ++X) are calculated in c.m.s.. The results show that, in a large range of (x_T, x_L), the calculated reaction cross section can be measured in current laboratory condition. And due to the properties of this reaction, i.e., large p_T photoproduction and direct photon pair emission, all of the backgrounds can be greatly suppressed.

     

CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD

The Yang-Mills field is quantized within the canonical formalism in covariant gauges. The interaction Lagrangian of X and X', i.e. the unphysical components of A_μ, is studied. In this Lagramgian there is only one term contributing to the S matrix elements between physical states. It is the source of the breaking of the unitarity of the physical S matrix. We get the gauge compensating term by solving a simple functional differential equation. If the gauge compensating term is added to the action, the S matrix in the physical state vector space can be expressed in a form which has no couplings of physical and unphysical particles, and so the physical S matrix is gauge independent and unitary.     

SPIN GAINT RESONANCE AND CORE POLARIZATION EFFECTS

The effects of the coupling term between field（Y₀σ₁）_1v and r²（Y₂σ₁）_1v coming fromtensor operator are discussed for the spin gaint dipole resonance.The effects of inclu-ding the field r^λ+1(Y_λ+1σ₁)_λv on the spin gaint multipole resonance and core polariza-tion are considered.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS (Ⅳ) MANY-BODY FORCES

It is shown that even if the nucleon-nucleon interactions contain many-body forces,the discrete energy eigenvalues ε_γ determined by the non-hermitian sp potential u_αβ=M_αβ（ε_β）still possess the following properties:G_γα（ε_γ）=∞,for at least one α,Since the points at which G_γα（ω） tends to ∞ areeither its poles or the heads of its branch cuts (where G_γα（ω） is log-divergent),itfollows that ε_γ are real and satisfy the relation.ε_γ=±[E_nγ（N±1）-E₀（N）].     

THE STUDY OF SOME NON-SOLATED RESONANCES FOR THE 23Na （p,α）20Ne REACTION

The excitation functions of the ²³Na（p,α₀）²⁰Ne_g·s.and the ²³Na（p,α₁）²⁰Ne_lst reae-tion have been measured from E_p=1 to 2.5 MeV at θ_L=30°,150° and 30°,respectively.Around the resonance at 2.171 MeV,the excitation functions of the（p,α₀）reactionhave been measured at 12 angles,then,some angular distributions have been obtained from these excitation functions.In addition,the angular distribution of the（p,α₀）reaction for the resonance at 2.171 MeV has also been measured directly at energy ofthe resonance peak of the excitation function at 150°.For the resonance at 2.117MeV,the angular distribution have been measured at two energies,one at the energyof the resonance peak of the excitation function at 150°,another at the energy of thehalf maximum point of the resonance peak on the higher energy side.Around the re-sonance at 2.075 MeV,the excitation functions have been measured at 16 angles,andthe angular distribution has been obtained from three excitation functions.The an-gular distributions of the three resonances are not symmetric about 90°,and the posi-tions of the resonance peaks of these resonances varies with the angle of measurement.By means of the compound nucleus theory,discussions have been made for these non-solated resonances.     

A TWO-NUCLEON MODEL OF THE（p,π-） REACTION

In this paper,we suggest a two-nucleon model of the A（p,π^-） B reaction.Areduced formulation of the reactoin amplitude and a relation between the reactionamplitude and the nuclear structure are given.The differential cross section of ¹³C（p,π^-）¹⁴O_g.s,at E_P=185 MeV is calculated in the plane wave approximation.The results+s can explain the experimental data qualilatively.