[en] We address the question of whether there might exist a resonance in the nnΛ system, using a rank one separable potential formulation of the Hamiltonian. We explore the eigenvalues of the kernel of the Faddeev equation in the complex energy plane using contour rotation to allow us to analytically continue the kernel onto the second energy sheet. We follow the largest eigenvalue as the nΛ potentials are scaled and the nnΛ continuum is turned into a resonance and then into a bound state of the system.

[en] A brief review of the results obtained in the description of nuclear reactions in systems containing up to four nucleons in the approach based on the Faddeev equations is given. The methods for consideration of relativistic effects and their influence on observables are discussed.

No abstract available

[en] The authors propose an algebraic method to determine anomalous commutators, which constitute Faddeev's anomaly, for general dimensions. This method is verified explicitly in 1 + 5 dimensions

[en] This paper clarifies recent works on generalized Chern-Simons secondary characteristic classes, relevant cohomologies of gauge groups including Cech-de rham complex and their applications to cohomological analyses on the structure of anomalies. The author shows that the cohomology of several gauge groups is in fact a particular case of this approach

[en] We study the scattering theory associated with the one dimensional time dependent quantum Hamiltonian. This system has nontrivial scattering between channels if λ₁ and λ₂ are both positive. We calculate the Faddeev series for the wave operators of this system explicitly. From this calculation we directly prove asymptotic completeness and study the entire S-matrix. The Faddeev series for the charge transfer matrix elements of the S-matrix exhibit rather surprizing behavior for large values of v₁ - v₂

No abstract available

[en] From the angle of the calculation of constraints, we compare the Faddeev-Jackiw method with Dirac-Bergmann algorithm, study the relations between the Faddeev-Jackiw constraints and Dirac constraints, and demonstrate that Faddeev-Jackiw method is not always equivalent to Dirac method. For some systems, under the assumption of no variables being eliminated in any step in Faddeev-Jackiw formalism, except for the Dirac primary constraints, we are possible to get some Dirac secondary constraints which do not appear in the corresponding Faddeev-Jackiw formalism, which will result in the contradiction between Faddeev-Jackiw quantization and Dirac quantization. At last, accordingly, we propose a modified Faddeev-Jackiw method which keeps the equivalence between Dirac-Bergmann algorithm and Faddeev-Jackiw method. However, one point must be stressed that the Faddeev-Jackiw method and quantization in this paper is these mentioned in [J. Barcelos-Neto, C. Wotzasek, Mod. Phys. Lett. A 7 (1992) 1737], not the initial Faddeev-Jackiw method mentioned in [L. Faddeev, R. Jackiw, Phys. Rev. Lett. 60 (1988) 1692], which is completely on basis of Darboux transformation, and must have the elimination of variables in every step of that, so it is reasonable that the constraints in this Faddeev-Jackiw method is fewer than the Dirac secondary constraints. Thus, we overcome the difficulty of the Non-equivalence of the Faddeev-Jackiw method and Dirac-Bergmann algorithm, and make the equivalence of the Faddeev-Jackiw method and Dirac-Bergmann algorithm restored

[en] The asymptotics of an infinite system of radial Faddeev equations corresponding to 2→3 breakup processes in investigated. It is shown that the solutions of the infinite system and of the system which is obtained by angular momentum cutoff have different asymptotics. Unlike the finite system, the asymptotics of the infinite system depends on characteristics of particles (on masses and charges) and also on the geometry of the process

[en] The methods presently proposed for the three body problem in quantum mechanics, using the Faddeev approach for proving the asymptotic completeness, come up against the presence of new singularities when the potentials considered v(α)(x(α)) for two-particle interactions decay less rapidly than /x(α)/^-2; and also when trials are made for solving the problem with a representation space whose dimension for a particle is lower than three. A method is given that allows the mathematical approach to be extended to three body problem, in spite of singularities. Applications are given