Banca de DEFESA: MATHEUS DA CUNHA PINTO

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE: MATHEUS DA CUNHA PINTO
DATA: 27/07/2026
HORA: 10:00
LOCAL: Remota
TÍTULO: Renormalização e cálculo de expoentes críticos para teorias de campos escalares do tipo λϕ3 em espaços-tempos com quebra da simetria de Lorentz
PALAVRAS-CHAVES: Teoria de campo escalar λϕ3; Expoentes críticos; Grupo de renormalização; Expansão em ε; Quebra da simetria de Lorentz; Universalidade.
PÁGINAS: 82
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

We investigate the renormalization and calculation of critical exponents in the scalar field theory of the λϕ3 type, formulated inspacetimes with explicit Lorentz-symmetry violation (LV). The starting point is the canonical theory in d = 6 − ε dimensions, the uppercritical dimension at which the cubic interaction is marginally relevant. Building on the foundational concepts of quantum field theory,we systematically construct the renormalization constants Zϕ, Zm2 , and Zλ up to two loops, employing dimensional regularization inthe minimal subtraction (MS) scheme. For the general case of an N-component field with the Potts-model interaction tensor dijk,we derive the relevant tensor contractions bα = (N + 1)2(N − 1), bβ = (N + 1)2(N − 2), and bγ = (N + 1)6 − 6(N + 1)5 + 10(N + 1)4,and obtain the beta function together with the anomalous dimensions. The non-trivial fixed point u∗(ε) yields the universal critical
exponents η(ε) and ν(ε). The special cases N = 1 (Yang–Lee edge singularity) and N → 0 (percolation) are examined individually,and numerical estimates in physical dimensions are obtained via Padé approximants [1, 1], with a discussion of the limitations imposedby the asymptotic nature of the ε-expansion. The extension to the LV scenario is performed by introducing a small, symmetric,
constant background tensor Kμν, with |Kμν| ≪ 1. The modified propagator admits a perturbative expansion in Kμν; we show that eachindependent loop-momentum integration introduces a multiplicative factor Π ≡ 1 − 12Kμνδμν, so that an L-loop diagram carries ΠL.
Consequently, the LV renormalization constants satisfy ZLV = ZLI(u → uΠ1/2), and the non-trivial fixed point shifts to u∗2LV = u∗2LI/Π.The central result of the dissertation is that, upon evaluating the anomalous dimensions at the shifted fixed point, all factors of Π cancelexactly, yielding critical exponents identical to those of the Lorentz-invariant theory: ηLV = ηLI and νLV = νLI, to two-loop order and for
|Kμν| ≪ 1. This outcome is interpreted as a direct consequence of the universality principle: the kinetic-sector Lorentz violation doesnot modify the internal symmetry that defines the universality class and is therefore irrelevant at the critical fixed point.

MEMBROS DA BANCA:
Externo à Instituição - 749.***.***-00 - EDILBERTO OLIVEIRA SILVA - UFMA
Interno - 1446938 - FRANCISCO WELINGTON DE SOUSA LIMA
Interno - 3331689 - HELDER ALEXANDER SANTOS E COSTA
Externo ao Programa - 3430956 - JORGIVAN MORAIS DIAS
Presidente - 1654258 - PAULO RENATO SILVA DE CARVALHO