1998/11/17 by J. Manjavidze, Manjavidze, J., A. N. Sissakian +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum and Classical Electrodynamics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9811160
61p., no figures, LaTex. To be published by parts in Theor. and Math. Phys
arxiv created 1998/11/17 · openalex publication_date 1998/11/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper contains successive description of the strong-coupling perturbation theory. Formal realization of the idea is based on observation that the path-integrals measure for absorption part of amplitudes \R is Diracian (\d-like). New form of the perturbation theory achieved mapping the quantum dynamics in the space WG of (action, angle) type collective variables. It is shown that the transformed perturbation theory contributions are accumulated on the boundary \pa WG, i.e. are sensible to the topology of factor space WG and,therefore, to the theory symmetry group G. The abilities of our perturbation theory are illustrated by examples from quantum mechanics and field theory. Considering the Coulomb potential 1/|x| the total reduction of quantum degrees of freedom is demonstrated mapping the dynamics in the (angle, angular momentum, Runge-Lentz vector) space. To solve the (1+1)-dimensional sin-Gordon model the theory is considered in the space (coordinates, momenta) of solitons. It is shown the total reduction of quantum degrees of freedom and, in result, there is not multiple production of particles. This result we interpret as the S-matrix form of confinement. The scalar O(4,2)-invariant field theoretical model is quantized in the WO=O(4,2)/O(4) × O(2) factor manifold. It is shown that the corresponding \R is nontrivial because of the scale invariance breaking.