Critical Exponents from the Resummed Effective Potential of the $$({\frac{g}{4}}\phi^{4}-J\phi)_{1+1}$$ Scalar Field Theory

2007 ◽  
Vol 46 (6) ◽  
pp. 1617-1635
Author(s):  
Abouzeid. M. Shalaby ◽  
S. T. El-Basyouny
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Critical Exponents ◽  
Scalar Field Theory

scholarly journals All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

2016 ◽  
Vol 30 (03) ◽  
pp. 1550259 ◽  
Author(s):  
Paulo R. S. Carvalho
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Critical Exponents ◽  
Lorentz Violation ◽  
Mathematical Explanation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Loop Order ◽  
Scalar Field Theory ◽  
Loop Level

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating (LV) O(N) self-interacting [Formula: see text] scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading loop order and later in a proof by induction up to any loop level, the respective [Formula: see text]-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.

scholarly journals Effective potential in scalar field theory

1987 ◽  
Vol 35 (10) ◽  
pp. 3187-3192 ◽  
Author(s):  
Kerson Huang ◽  
Efstratios Manousakis ◽  
Janos Polonyi
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Scalar Field Theory

scholarly journals Coleman–Weinberg potential in p-adic field theory

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Dmitry S. Ageev ◽  
Andrey A. Bagrov ◽  
Askar A. Iliasov
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Space Time ◽  
The Other ◽  
Quantum Corrections ◽  
Real Field ◽  
Scalar Field Theory ◽  
Other Hand ◽  
Peculiar Behavior

AbstractIn this paper, we study $$\lambda \phi ^4$$ λ ϕ 4 scalar field theory defined on the unramified extension of p-adic numbers $${\mathbb {Q}}_{p^n}$$ Q p n . For different “space-time” dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman–Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, $$p \rightarrow 1$$ p → 1 and $$p \rightarrow \infty $$ p → ∞ . We show that the $$p\rightarrow 1$$ p → 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the $$p\rightarrow \infty $$ p → ∞ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.

scholarly journals Scalar field theory limits of bosonic string amplitudes

2000 ◽  
Vol 579 (1-2) ◽  
pp. 379-410 ◽  
Author(s):  
Alberto Frizzo ◽  
Lorenzo Magnea ◽  
Rodolfo Russo
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Bosonic String ◽  
Scalar Field Theory ◽  
String Amplitudes

On causality in polymer scalar field theory

2011 ◽  
Author(s):  
Angel A. García-Chung ◽  
Hugo A. Morales-Técotl ◽  
Luis Arturo Ureña-López ◽  
Hugo Aurelio Morales-Técotl ◽  
Román Linares-Romero ◽  
...  
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Field Theory
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