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Scaling Limits of Lattice Quantum Fields by Wavelets
Vincenzo Morinelli1, Gerardo Morsella2, Alexander Stottmeister3
1Department of Mathematics, FAU Erlangen-Nürnberg, Cauerstraße 11, 91058 Erlangen, Germany.
Communications in Mathematical Physics
|November 15, 2021
Summary
This study introduces a novel renormalization group scheme for lattice quantum field theories using operator algebras and Daubechies
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Mathematical Physics
Background:
- Lattice quantum field theories require robust renormalization schemes.
- Existing methods like momentum shell and block-spin transformations have limitations.
Purpose of the Study:
- To develop a rigorous renormalization group (RG) scheme for lattice quantum field theories.
- To reformulate the RG as an inductive system of scaling maps between operator algebras.
Main Methods:
- Utilized operator algebras to define the renormalization group.
- Constructed scaling maps for scalar lattice fields employing Daubechies' wavelets.
- Investigated the inductive limit of free lattice ground states.
Main Results:
- Demonstrated the existence of the inductive limit of free lattice ground states.
- Showed that the limit state corresponds to the massive continuum free field.
- Identified lattice fields with continuum fields smeared by Daubechies' scaling functions.
Conclusions:
- The proposed operator algebra-based RG scheme provides a rigorous framework for lattice field theories.
- Daubechies' wavelets are effective tools for constructing scaling maps in this context.
- The method offers an alternative perspective compared to traditional renormalization techniques.
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