1978 Vol. 2, No. 2
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Abstract:
The gauge field theory is formulated via loop phase factors with a fixed point O as their initial and final point. Let G be the gauge group. When the base space is the Minkowski space E4, we introduce a set of standard paths Ox （for example, the set of line segments Ox）, where x is arbitrary. The phase factor for the infinitesimal loop Oxx+dxO corresponds to an element in the Lie algebra g and can be expressed as a g-valued differential form k（x, dx） which satisfies the following conditions of consistency （a） k（O, dx）=0, （b） k（x, v）=0, where v is the tangential vector of Ox at x. It is shown that an equivalent class of gauge fields is determined by k（x, dx） or （ad a） k（x, dx） where a is a fixed element of G. Hence if we adopt k（x, dx） for the fundamental physical quantity of a gauge field then a great part of gauge indefiniteness is eliminated. Moreover if the phase factors Φxo for standard paths Ox are given then the phase factors for differential arcs x x+dx are easily calculated, and hence a gauge field in the equivalent class is extracted. We call the set of phase factors for standard paths a gauge and k（x, dx） may be interpretated as the gauge potential under a special gauge under which Φxo=the unit element of G.The method is useful in considering the equivalence problem and the spacetime symmetry of gauge fields. For example, it is quite easy to determine all spherically symmetric gauge fields if they are free of singularities. By using the method it can also be proved that if two gauge fields have the same gauge and the same field strength then their gauge potentials are equal to each other. Consequently, under a given gauge in the above sense the field strength determines the gauge potential completely.For a general base manifold Mn, every equivalent class of gauge fields over Mn can be defined by loop phase factors also. In this case, Mn is expressed as the sum of a set of neighborhoods each of which is homeomorphic to the Euclidean space. The standard paths are constructed according a certain rule, the phase factors for standard differential loops are also introduced. The transition functions and gauge potentials of a gauge field in the given equivalent class are derived as the phase factors for some finite loops and standard differential loops respectively. Further it is remarkable that a global gauge field is determined completely by the field strength and some discrete loop factors, if the phase factors for the standard paths are gwen.In mathematical terminology principal G-bundle structure as well as a connection in it is determined by the holonomic mapping which maps the set of loops through a fixed point into the group G, provided the mapping is differentible in a certain.The author is very grateful to Prof. Yang Chen Ning for many helpful discussions.
The gauge field theory is formulated via loop phase factors with a fixed point O as their initial and final point. Let G be the gauge group. When the base space is the Minkowski space E4, we introduce a set of standard paths Ox （for example, the set of line segments Ox）, where x is arbitrary. The phase factor for the infinitesimal loop Oxx+dxO corresponds to an element in the Lie algebra g and can be expressed as a g-valued differential form k（x, dx） which satisfies the following conditions of consistency （a） k（O, dx）=0, （b） k（x, v）=0, where v is the tangential vector of Ox at x. It is shown that an equivalent class of gauge fields is determined by k（x, dx） or （ad a） k（x, dx） where a is a fixed element of G. Hence if we adopt k（x, dx） for the fundamental physical quantity of a gauge field then a great part of gauge indefiniteness is eliminated. Moreover if the phase factors Φxo for standard paths Ox are given then the phase factors for differential arcs x x+dx are easily calculated, and hence a gauge field in the equivalent class is extracted. We call the set of phase factors for standard paths a gauge and k（x, dx） may be interpretated as the gauge potential under a special gauge under which Φxo=the unit element of G.The method is useful in considering the equivalence problem and the spacetime symmetry of gauge fields. For example, it is quite easy to determine all spherically symmetric gauge fields if they are free of singularities. By using the method it can also be proved that if two gauge fields have the same gauge and the same field strength then their gauge potentials are equal to each other. Consequently, under a given gauge in the above sense the field strength determines the gauge potential completely.For a general base manifold Mn, every equivalent class of gauge fields over Mn can be defined by loop phase factors also. In this case, Mn is expressed as the sum of a set of neighborhoods each of which is homeomorphic to the Euclidean space. The standard paths are constructed according a certain rule, the phase factors for standard differential loops are also introduced. The transition functions and gauge potentials of a gauge field in the given equivalent class are derived as the phase factors for some finite loops and standard differential loops respectively. Further it is remarkable that a global gauge field is determined completely by the field strength and some discrete loop factors, if the phase factors for the standard paths are gwen.In mathematical terminology principal G-bundle structure as well as a connection in it is determined by the holonomic mapping which maps the set of loops through a fixed point into the group G, provided the mapping is differentible in a certain.The author is very grateful to Prof. Yang Chen Ning for many helpful discussions.
Abstract:
Assuming that the interactions between stratons are caused by exchanging various particles, we propose a nearly-flat-bottom potential between the stratons, which is responsible to the formation of the hadrons. Using this potential the wave function of the pseudoscalar meson is calculated and compared with those obtained by using other potentials. The results show that the nearly-flat-bottom potential possesses some obviously reasonable features, in particular, it can lead to the formation of pions with physical radius.
Assuming that the interactions between stratons are caused by exchanging various particles, we propose a nearly-flat-bottom potential between the stratons, which is responsible to the formation of the hadrons. Using this potential the wave function of the pseudoscalar meson is calculated and compared with those obtained by using other potentials. The results show that the nearly-flat-bottom potential possesses some obviously reasonable features, in particular, it can lead to the formation of pions with physical radius.
Abstract:
In this paper we introduce the concept of "same order" in the perturbution expansion of the quatized composite field theory which is different from single particle theory. For example, in the case of Q. E. D., "same order" is defined by means of a coupling constant, but here it closely relates the operators occuring in the B. S. equations. Feymann graphs of the "same order" are defined for different kinds of transitions in the composite field theory. Finally, we prove that guage invariance is a natural result as long as all "same order" Feymann graphs are calculated for an electromagnetic transition between composite particles.
In this paper we introduce the concept of "same order" in the perturbution expansion of the quatized composite field theory which is different from single particle theory. For example, in the case of Q. E. D., "same order" is defined by means of a coupling constant, but here it closely relates the operators occuring in the B. S. equations. Feymann graphs of the "same order" are defined for different kinds of transitions in the composite field theory. Finally, we prove that guage invariance is a natural result as long as all "same order" Feymann graphs are calculated for an electromagnetic transition between composite particles.
Abstract:
Based on an analysis of the Bayesian posteriori density method and the Non-Bayesian confidence interval method for parameter estimation, the concept and a computation formula for the confidence density are introduced from the confidence interval. It is shown that the confidence density distribution is a complete description of the result of the Non-Bayesian parameter estimation and possesses a definite probability meaning. As an example to show its application, a statistical inference to the mass of a charged particle is made.
Based on an analysis of the Bayesian posteriori density method and the Non-Bayesian confidence interval method for parameter estimation, the concept and a computation formula for the confidence density are introduced from the confidence interval. It is shown that the confidence density distribution is a complete description of the result of the Non-Bayesian parameter estimation and possesses a definite probability meaning. As an example to show its application, a statistical inference to the mass of a charged particle is made.
Abstract:
Excitation functions for Fr and At isotopes produced in 12C on 209Bi had been measured in the energy range 60—72 MeV. It was quite obvious that 213Fr and 214Fr were formed by the reactions 209Bi (12C,4n) 217Ac and 209Bi (12C,3n) 218Ac following the a decay of the Ac isotopes respectively, and 214mFr was produced probably by compound nucleus evaporation of neutrons and an α particle, i.e. (12C, α 3n). 211At was mainly contributed by a multi-nucleon transfer reaction （e.g. 8Be transfer）. The experimental data for neutron evaporation reaction were fitted by the Jackson formula.
Excitation functions for Fr and At isotopes produced in 12C on 209Bi had been measured in the energy range 60—72 MeV. It was quite obvious that 213Fr and 214Fr were formed by the reactions 209Bi (12C,4n) 217Ac and 209Bi (12C,3n) 218Ac following the a decay of the Ac isotopes respectively, and 214mFr was produced probably by compound nucleus evaporation of neutrons and an α particle, i.e. (12C, α 3n). 211At was mainly contributed by a multi-nucleon transfer reaction （e.g. 8Be transfer）. The experimental data for neutron evaporation reaction were fitted by the Jackson formula.
Abstract:
Mica track detectors were used for the measurement of evaporation residues and fission fragments of compound nuclei formed in 12C+27Al, 12C+209Bi and 14N+Pb reactions. The complete fusion cross-sections and excitation functions were then obtained. By using the sharp cut-off model approximation, the values of the critical angular momenta were extracted from the complete fusion cross-sections. The results obtained were compared with the calculations based on current theories for critical angular momentum; they were found to agree within experimental uncertainties.
Mica track detectors were used for the measurement of evaporation residues and fission fragments of compound nuclei formed in 12C+27Al, 12C+209Bi and 14N+Pb reactions. The complete fusion cross-sections and excitation functions were then obtained. By using the sharp cut-off model approximation, the values of the critical angular momenta were extracted from the complete fusion cross-sections. The results obtained were compared with the calculations based on current theories for critical angular momentum; they were found to agree within experimental uncertainties.
Abstract:
A new formalism of the nuclear many-body problem is established in which one ean work with various physical state vector spaces consisting of both Fermions and Bosons, all being equivalent to the original one consisting only of Fermions.With the help of the usual commutation relations and anticommutation relations between the annihilation and creation operators of Boson and Fermion, a generalized state vector space is established, which contains all the physical spaces each being equivalent to the original physical space in terms of pure Fermion operators. Transformation between the state vectors in various equivalent physical spaces are constructed. Basic operators in the original state space are transformed into effective operators in the new physical spaces.
A new formalism of the nuclear many-body problem is established in which one ean work with various physical state vector spaces consisting of both Fermions and Bosons, all being equivalent to the original one consisting only of Fermions.With the help of the usual commutation relations and anticommutation relations between the annihilation and creation operators of Boson and Fermion, a generalized state vector space is established, which contains all the physical spaces each being equivalent to the original physical space in terms of pure Fermion operators. Transformation between the state vectors in various equivalent physical spaces are constructed. Basic operators in the original state space are transformed into effective operators in the new physical spaces.
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