Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU(2) Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of...Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU(2) Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of the Faddeev model axe discussed. The solutions are classified by the 2, the new multisoliton solutions are obtained and the pipe shape found. first Chern number. When the Chern number equals distribution of the energy density of the solutions are展开更多
Using the Faddeev-Jackiw (FJ) quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which ...Using the Faddeev-Jackiw (FJ) quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac's method.展开更多
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1+n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the ...We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1+n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.展开更多
In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels...In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent.The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles(bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length,phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.展开更多
The Faddeev AGS equations for the coupled-channels ■NN-πΣN system with quantum numbers I=1/2 and S=0 are solved. Using separable potentials for the ■N-πΣ interaction, we calculate the transition probability for ...The Faddeev AGS equations for the coupled-channels ■NN-πΣN system with quantum numbers I=1/2 and S=0 are solved. Using separable potentials for the ■N-πΣ interaction, we calculate the transition probability for the(YK)I=0 + N→πΣN reaction. The possibility to observe the trace of the K-pp quasi-bound state in πΣN mass spectra was studied. Various types of chiral-based and phenomenological potentials are used to describe the ■N-πΣ interaction. Finally, we show that we can observe the signature of the K-pp quasi-bound state in the mass spectra, as well as the trace of branch points in the observables.展开更多
Effective lambda-proton and lambda-neutron potentials,restored from theoretical scattering phases through Gel'fand–Levitan–Marchenko theory,are tested on a lambda hypertriton through three-body calculations.The ...Effective lambda-proton and lambda-neutron potentials,restored from theoretical scattering phases through Gel'fand–Levitan–Marchenko theory,are tested on a lambda hypertriton through three-body calculations.The lambda hypertriton is treated as a three-body system consisting of lambda-proton,lambda-neutron and proton–neutron subsystems.Binding energy and root mean square radius are computed for the ground state of lambda hypertriton(Jp=12+).In coordinate space,the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations.By solving the eigenvalue problem derived from this set of coupled hyperradial equations,the binding energy and root mean square matter radius computed are found to be-2.462 MeV and 7.00 fm,respectively.The potentials are also shown to display a satisfactory convergence behaviour.展开更多
We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is gi...We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given. We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method. Moreover, it is simpler than the usual one if one needs to obtain new secondary constraints. Therefore, the improved Faddeev-Jackiw method is essential. Meanwhile, we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.展开更多
The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and s...The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undifferentiated wave components in the non-linearities, which somehow causes extra difficulties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou(2011) with small, regular, and compactly supported initial data, using Klainerman’s vector field method enhanced by a novel angular-radial anisotropic technique.In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou(2011). The proof relies on an improved L2norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.展开更多
基金National Natural Science Foundation of China under Grant No.10601031the Natural Science Foundation of Shanghai Municipal Education Commission under Grant No.05LZ08the Foundation of Shanghai University of Electric Power under Grant No.K2005-01
文摘Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU(2) Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of the Faddeev model axe discussed. The solutions are classified by the 2, the new multisoliton solutions are obtained and the pipe shape found. first Chern number. When the Chern number equals distribution of the energy density of the solutions are
文摘Using the Faddeev-Jackiw (FJ) quantization method, this paper treats the CP^1nonlinear sigma model with ChernSimons term. The generalized FJ brackets are obtained in the framework of this quantization method, which agree with the results obtained by using the Dirac's method.
基金The first author is partly supported by National Natural Science Foundation of China (Grants Nos. 10801029 and 10911120384), FANEDD, Shanghai Rising Star Program (10QA1400300), SGST 09DZ2272900 and SRF for ROCS, SEM the second author is partly supported by an NSF grant the third author is partly supported by the National Natural Science Foundation of China (Crant No. 10728101), the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the "111" project (B08018) and SGST 09DZ2272900Acknowledgements Part of the work was carried out when Zhen Lei was visiting the Courant Institute. He would like to thank Professor Fanghua Lin for his hospitality.
文摘We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1+n to the unit sphere S2, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.
文摘In this work, the Faddeev equations for three-body scattering at arbitrary angular momentum are exactly solved and the transition matrices for some transition processes, including scattering and rearrangement channels are formulated in terms of free-particle resolvent matrix. A generalized Yamaguchi rank-two nonlocal separable potential has been used to obtain the analytical expressions for partial wave scattering properties of a three-particle system. The partial-wave analysis for some transition processes in a three-particle system is suggested. The partial-wave three-particle transition matrix elements have been constructed via knowledge of the matrix elements of the free motion resolvent.The calculation of a number of scattering properties of interest of the system such as transition matrix and its poles(bound states and resonances) and consequently other related quantities like scattering amplitudes, scattering length,phase shifts and cross sections are feasible in a straightforward manner. Moreover, we obtain a new analytical expression for the third virial coefficient in terms of three-body transition matrix.
文摘The Faddeev AGS equations for the coupled-channels ■NN-πΣN system with quantum numbers I=1/2 and S=0 are solved. Using separable potentials for the ■N-πΣ interaction, we calculate the transition probability for the(YK)I=0 + N→πΣN reaction. The possibility to observe the trace of the K-pp quasi-bound state in πΣN mass spectra was studied. Various types of chiral-based and phenomenological potentials are used to describe the ■N-πΣ interaction. Finally, we show that we can observe the signature of the K-pp quasi-bound state in the mass spectra, as well as the trace of branch points in the observables.
文摘Effective lambda-proton and lambda-neutron potentials,restored from theoretical scattering phases through Gel'fand–Levitan–Marchenko theory,are tested on a lambda hypertriton through three-body calculations.The lambda hypertriton is treated as a three-body system consisting of lambda-proton,lambda-neutron and proton–neutron subsystems.Binding energy and root mean square radius are computed for the ground state of lambda hypertriton(Jp=12+).In coordinate space,the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations.By solving the eigenvalue problem derived from this set of coupled hyperradial equations,the binding energy and root mean square matter radius computed are found to be-2.462 MeV and 7.00 fm,respectively.The potentials are also shown to display a satisfactory convergence behaviour.
文摘We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given. We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method. Moreover, it is simpler than the usual one if one needs to obtain new secondary constraints. Therefore, the improved Faddeev-Jackiw method is essential. Meanwhile, we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.
基金supported by the National Natural Science Foundation of China(No.11725102)the China Postdoctoral Science Foundation(No.2021M690702)+1 种基金the National Support Program for Young Top-Notch TalentsShanghai Science and Technology Program(Nos.21JC1400600,19JC1420101)。
文摘The Faddeev model is a fundamental model in relativistic quantum field theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undifferentiated wave components in the non-linearities, which somehow causes extra difficulties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou(2011) with small, regular, and compactly supported initial data, using Klainerman’s vector field method enhanced by a novel angular-radial anisotropic technique.In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou(2011). The proof relies on an improved L2norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.