Martin Gutierrez, Alejandro
(2022)
Multi-scalar critical theories: first steps for a non
perturbative functional renormalization group
analysis.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Physics [LM-DM270], Documento ad accesso riservato.
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Abstract
In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.
Abstract
In this work the fundamental ideas to study properties of QFTs with the functional Renormalization Group are presented and some examples illustrated. First the Wetterich equation for the effective average action and its flow in the local potential approximation (LPA) for a single scalar field is derived. This case is considered to illustrate some techniques used to solve the RG fixed point equation and study the properties of the critical theories in D dimensions. In particular the shooting methods for the ODE equation for the fixed point potential as well as the approach which studies a polynomial truncation with a finite number of couplings, which is convenient to study the critical exponents. We then study novel cases related to multi field scalar theories, deriving the flow equations for the LPA truncation, both without assuming any global symmetry and also specialising to cases with a given symmetry, using truncations based on polynomials of the symmetry invariants. This is used to study possible non perturbative solutions of critical theories which are extensions of known perturbative results, obtained in the epsilon expansion below the upper critical dimension.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Martin Gutierrez, Alejandro
Relatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Quantum Field Theory,Critical phenomena,Effective action,Functional Renormalization Group,Wetterich-Morris Equation,Multicritical Scalar Models,Local Potential Approximation,Fixed Point,Critical Exponents
Data di discussione della Tesi
31 Maggio 2022
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Martin Gutierrez, Alejandro
Relatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
Quantum Field Theory,Critical phenomena,Effective action,Functional Renormalization Group,Wetterich-Morris Equation,Multicritical Scalar Models,Local Potential Approximation,Fixed Point,Critical Exponents
Data di discussione della Tesi
31 Maggio 2022
URI
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