Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-11-17
Physics
High Energy Physics
High Energy Physics - Theory
61p., no figures, LaTex. To be published by parts in Theor. and Math. Phys
Scientific paper
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 $W_G$ of (action, angle) type collective variables. It is shown that the transformed perturbation theory contributions are accumulated on the boundary $\pa W_G$, i.e. are sensible to the $topology$ of factor space $W_G$ 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 $W_O=O(4,2)/O(4) {\times} O(2)$ factor manifold. It is shown that the corresponding $\R$ is nontrivial because of the scale invariance breaking.
Manjavidze Joseph
Sissakian Aleksey
No associations
LandOfFree
Fields topology and observables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fields topology and observables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fields topology and observables will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-187502