Banca de QUALIFICAÇÃO: MATHEUS DA CUNHA PINTO

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
DISCENTE: MATHEUS DA CUNHA PINTO
DATA: 28/08/2025
HORA: 10:00
LOCAL: Remota (On-line)
TÍTULO: Renormalização e cálculo de expoentes críticos para teorias de campos escalares do tipo λφ3 em Espaços-Tempos com Violação da Simetria de Lorentz
PALAVRAS-CHAVES: Quantização; Renormalização; Diagramas de Feynman; Expoentes Crí- ticos; Quebra de Simetria de Lorentz
PÁGINAS: 103
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

We investigate the renormalization and calculation of critical exponents in scalar field
theories of the λφ3

type formulated in spacetimes with explicit Lorentz-symmetry viola-
tion. We begin by laying out the essential concepts of quantum field theory: the canonical

quantization of fields, the path-integral approach to amplitudes, and the graphical for-
malism of Feynman diagrams. This foundation makes transparent the rules governing

particle interactions and the buildup of fluctuations at each loop order.

Next, we introduce the λφ3 model, emphasizing its cubic interaction and its role in des-
cribing quantum fluctuations near the critical point. Through perturbative expansion
and S-matrix construction, loop divergences are identified and regularized via dimensio-
nal regularization. Renormalization is then carried out in the minimal subtraction (MS)
1scheme by introducing counterterms for field normalization, mass, and coupling constant,
thereby rendering all Green’s functions finite.
We then perform a renormalization-group analysis based on the ε-expansion, from which
we derive the β-functions and anomalous dimensions (γ-functions) needed to compute the
universal critical exponents ν and η. These exponents quantify how physical observables
scale in the vicinity of the phase transition.
To extend our study, we modify the underlying metric tensor by adding Lorentz-violating
operators. This alteration deforms the propagators and vertex rules in momentum space,
which in turn changes the structure of both the loop integrals and the RG flow equations.
We calculate the Lorentz-violating contributions to the β and γ functions and extract
the corrected values of ν and η. A comparative discussion then highlights how explicit
Lorentz-symmetry violation alters the universal scaling laws, quantifying the deviations
from the Lorentz-invariant fixed point. Finally, we present the physical interpretation of
these results.

MEMBROS DA BANCA:
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