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Regularization of diagrammatic series with zero convergence radius
Lode Pollet1, Nikolay V Prokof'ev, Boris V Svistunov
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|January 15, 2011
Summary
Divergent perturbative expansions hinder studies of strongly interacting systems. This research introduces a convergent approximation method that preserves Feynman
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- Perturbative expansions in quantum field theory often diverge for macroscopic systems.
- Dyson's collapse argument highlights the limitations of direct Feynman diagrammatic techniques for strongly correlated systems.
Purpose of the Study:
- To address the divergence problem in perturbative expansions.
- To develop a method for controllable studies of strongly interacting systems.
Main Methods:
- Replacing the original model with a convergent sequence of successive approximations.
- Maintaining the diagrammatic structure of Feynman's technique.
Main Results:
- The proposed method yields a convergent perturbative series.
- The approach is demonstrated using the zero-dimensional |ψ|⁴ theory as a model.
Conclusions:
- The developed technique offers a viable solution to the divergence issue in perturbative expansions.
- This method enables controllable studies of strongly interacting systems using a modified diagrammatic approach.
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