Extension Of The Renormalizable Theory

In this paper, we have deeply studied the renormalization issues of the renormalizable theory and the nonrenormalizable effective field theory in the quantum hadron dynamics, and the mass characteristics of the isovector mesons in asymmetric nuclear matter. For the renormalizable theory, theoretically there have been various renormalization method which can systematically resolve renormalization issues of higher-order quantum correction at present. However, for the nonrenormalizable theory, in principle, we can't fully eliminate the ultraviolet divergence produced by the higher-order quantum correction, which is because the superficial degree of divergence of Feynman diagram generated by the non-renormalizable interaction will grow with the order of perturbation. According to the renormalization theory, we need introduce an infinite number of counterterms in the Lagrangian to cancel the ultraviolet divergence caused by this interaction; while for the renormalizable interaction, only a finite number of counterterms is necessary. From the credibility of theoretical predictions and the convergence, there is essential difference between the renormalizable and the nonrenormalizable theory. Therefore, the nonrenormalizable effective field theory encountered insurmountable difficulties on the renormalization issues.This paper presents a new renormalization method, namely, use the formula of dispersion relations and its promotion formula to resolve the real part of the Feynman integral via its finite imaginary part, and then obtain the contribution of the whole Feynman diagram. Take example forπmodel, considering the two cases ofπ?N pseudoscalar coupling and pseudovector coupling, we detailedly derive the regular self-energy formulas of the nuclear and meson and their spectral function expression under the one loop approximation. Due to perturbation theory is not applicable in the strong interaction, we take into account infinite series summation of the exchange items using the Dyson-Schwinger equations, which lies in self-consistency problem of the nuclear propagator in calculation. Comparing with the results of self-energy and spectral function of nuclear and meson with that obtained by the other renormalization method, we find that the effect of our regularization method is the same as one of the scheme combined dimensional regularization with on-shell regularization conditions. Besides, the method does not need to consider such process as regularization of the Feynman integral calculations and the introduction of counter-term. Therefore, the calculation is convenient and simple. From the calculation results, the nuclear propagator has obvious self-consistent effect, and the self-consistency of meson propagator is not important. For the two cases of pseudo-scalar coupling and pseudo-vector coupling, whether to the nuclear self-energy and its spectral function, or to the meson self-energy and its spectral function, the results are significant differences. We still need calculate the observable quantity to judge which kind of coupling form should be more agree with the physics on earth. In addition, we find from the calculation that the method only applies to renormalizable interaction. For the nonrenormalizable theory, such as theπ?N pseudo-vector coupling, when exchange self-energy of the divergent second-order nucleon, this method will produce an extra free parameter, moreover, for the higher order self-energy, the more free parameters will be produced.This paper focuses on the research how to realize the extent of the renormalizable theory. Although in the whole course of the study, we have encountered many difficulties, but it is still very possible to realize the extension of the renormalizable theory finally. In this paper, we advance the new ideas such as selecting the effective Lagrangian form, dressed scheme, dressed propagator. Compared with the original free Lagrangian form, the effective Lagrangian of the hadron filed has a new term, which can be understood as self-interaction term or single-particle potential. Besides, along with decrease of the new parameter in the Lagrangian, the role of this term will become smaller. According to the dressed scheme and perturbation theory, the perturbation series can also be expanded with the dressed propagator instead of the bare ordinary propagator. The dressed propagator has better properties: compared with ordinary propagator, they have the same physical pole and residues, and they both haven't the non-physical poles in the limit complex plane, the dressed propagator agrees with the ordinary propagator in a very wide momentum region. All of conditions show that the dressed propagator can be regarded as a very good approximation of the ordinary propagator. In the large momentum region, the asymptotic behavior of the dressed propagator is much higher than that of the ordinary propagator. Just because of the asymptotic characteristic of the dressed propagator, almost all of the higher order Feynman diagram will automatically converge except for the individual Feynman diagram such as tadpole diagram. On the basis of the theory, the quantum field theory not including singular interactions built on the special relativity are all actually renormalizable theory, namely, the extension of the renormalizable theory have be realized. In this scheme, we examined the renormalizability of the pseudovector coupling of the pseudoscalar meson and the nucleon and the tensor coupling of the vector meson and the nucleon, and calculated the nuclear self-energy and meson self-energy under the one loop approximation, both of which are automatically convergent. In order to validate the feasibility of the scheme, we have calculated the effective mass ofρmeson in nuclear matter for the vector - tensor model, and examine the influence of the vacuum fluctuation on theρmass. The result shows that by properly adjust the coupling constant and parameter, we can obtain the data agree with the experimental data, while selecting different value of the new parameter in the Lagrangian, the curve ofρmeson mass along with the density of the nuclear matter will have obvious differences. All of them show thatρmeson mass decreases along with the density of the nuclear matter increases, however, the reduce speed is different.Because the isospin vector mesons will appear mass splitting phenomenon in the antisymmetric nuclei or nuclear matter, we use the QHD-II model to research the effective mass of theρmesons triplet in asymmetric nuclear matter, and derive the analytical formula of the effective mass of theρmesons. The calculated results show that the results will have a large difference whether take the Dirac Sea effect into account or not. In order to coincide with the experimental data, the effect of the Dirac Sea must be taken into account. In this condition, in the Pb-like nuclei and asymmetric nuclear matter, theρmeson triplet occur mass splitting phenomenon. The size of the mass split depends on the nuclear matter density and asymmetric parameters, among them, the dependence on the latter is more obvious. When the nuclear matter density is defined, the mass difference of theρmesons triplet will increase rapidly along with the increase of the asymmetric parameters. When the asymmetric parameters are defined, the mass difference of theρmesons triplet won't have too much change along with the increase of the nuclear matter density, however, in the different density region, the mass splitting mode of the three kinds ofρmesons, namely the array of the mass size will change. When the nuclear matter density and asymmetric parameter are taken some determined value, the three kinds ofρmeson mass splitting phenomenon may disappear. For the saturation density, the mass splitting phenomenon of theρmesons triplet is very similar to that of theπmesons for the pseudo-vector coupling. Therefore, the mass split is a generic feature of all the isovector meson.