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Hard noncommutative loops resummation
Luca Griguolo1, Massimo Pietroni
1Dipartimento di Fisica, Università di Parma, INFN-Gruppo Collegato di Parma, Parco Area delle Scienze, 7/A, I-43100 Parma, Italy.
Physical Review Letters
|February 28, 2002
Summary
This study proves ultraviolet renormalizability for noncommutative Euclidean g2phi4 theory using Wilsonian flow equations. It addresses infrared divergences via resummation, analogous to hard thermal loops in field theory.
Area of Science:
- Quantum Field Theory
- Noncommutative Geometry
- Mathematical Physics
Background:
- The Euclidean g2phi4 theory is a fundamental model in quantum field theory.
- Noncommutative geometry introduces novel structures to traditional field theories.
- Understanding the behavior of quantum field theories in both ultraviolet and infrared regimes is crucial.
Purpose of the Study:
- To investigate the ultraviolet renormalizability of the noncommutative Euclidean g2phi4 theory.
- To address the non-perturbative infrared sector of this theory.
- To compute next-to-leading order corrections to the self-energy.
Main Methods:
- Utilizing Wilsonian flow equations to prove ultraviolet renormalizability.
- Employing resummation techniques for leading infrared divergences in the two-point function.
- Calculating next-to-leading order corrections to the self-energy.
Main Results:
- Ultraviolet renormalizability is demonstrated to all orders in perturbation theory.
- A resummation method, analogous to hard thermal loops, is applied to the infrared sector.
- Next-to-leading order corrections yield O(g3) contributions in the massless case and O(g6logg2) in the massive case.
Conclusions:
- The noncommutative Euclidean g2phi4 theory is ultraviolet renormalizable.
- The infrared sector requires non-perturbative treatment, with specific corrections identified.
- The findings provide insights into the behavior of noncommutative quantum field theories.
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