Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking
Abstract
:1. Introduction
2. Related Works
3. Framework
3.1. The Model
3.2. Functional Renormalization Group Formalism
- , the regulator, plays the role of an effective mass, depending both on momenta and infrared cut-off k. It vanishes for high momenta with respect to k (), whereas low momenta modes are frozen, and decouple from long distance physics. Moreover, vanishes for , ensuring that all the modes are integrated out.
- The effective averaged Hamiltonian is defined from a slight modified version of the Legendre transform for free energy :
- The notation means second derivative with respect to M, the classical field defined as:
4. -Symmetry Breaking and Signal Detection
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Lahoche, V.; Ousmane Samary, D.; Tamaazousti, M. Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking. Symmetry 2022, 14, 486. https://doi.org/10.3390/sym14030486
Lahoche V, Ousmane Samary D, Tamaazousti M. Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking. Symmetry. 2022; 14(3):486. https://doi.org/10.3390/sym14030486
Chicago/Turabian StyleLahoche, Vincent, Dine Ousmane Samary, and Mohamed Tamaazousti. 2022. "Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking" Symmetry 14, no. 3: 486. https://doi.org/10.3390/sym14030486
APA StyleLahoche, V., Ousmane Samary, D., & Tamaazousti, M. (2022). Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking. Symmetry, 14(3), 486. https://doi.org/10.3390/sym14030486