NLO critical exponents of O(N) λ ϕ4 scalar field theories in curved spacetime

In this paper, we investigate analytically the conformal symmetry influence on the next-to-leading order radiative quantum corrections to critical exponents for massless O([Formula: see text]) [Formula: see text] scalar field theories in curved spacetime. We renormalize the theory by applying the Bogoliubov–Parasyuk–Hepp–Zimmermann (BPHZ) method. We find that the critical exponents are the same as that of flat spacetime, at least at the loop order considered. We argue that this result agrees perfectly with the universality hypothesis.

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Influence of exact Lorentz-violating mechanism on the critical exponents for massive q-deformed λϕ4 scalar field theory

International Journal of Modern Physics D ◽

10.1142/s0218271819501050 ◽

2019 ◽

Vol 28 (08) ◽

pp. 1950105

Author(s):

P. R. S. Carvalho ◽

M. I. Sena-Junior

Keyword(s):

Scalar Field ◽

Critical Exponents ◽

Field Theories ◽

Quantum Corrections ◽

Leading Order ◽

Independent Field ◽

Group Methods ◽

Breaking Mechanism ◽

Lorentz Symmetry Breaking ◽

Renormalization Group Methods

We probe the influence of Lorentz-violating mechanism, treated exactly, on the radiative quantum corrections to critical exponents for massive [Formula: see text]-deformed O([Formula: see text]) [Formula: see text] scalar field theories. We attain that task by employing three distinct and independent field-theoretic renormalization group methods. Firstly, we compute the critical exponents up to the finite next-to-leading order for then generalizing the results for any loop level. We show that the [Formula: see text]-deformed critical exponents are insensible to the Lorentz symmetry breaking mechanism thus agreeing with the universality hypothesis.

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Unconventional minimal subtraction and Callan–Symanzik methods for Lorentz-violating scalar field theories at all loop orders

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781850086x ◽

2018 ◽

Vol 15 (05) ◽

pp. 1850086 ◽

Cited By ~ 3

Author(s):

G. S. Silva ◽

P. R. S. Carvalho

Keyword(s):

Scalar Field ◽

Critical Exponents ◽

Field Theories ◽

Quantum Corrections ◽

Leading Order ◽

Minimal Subtraction ◽

Analytical Computation ◽

Induction Process ◽

Time In Literature ◽

First Time

We present an explicit analytical computation of the quantum corrections, at next-to-leading order, to the critical exponents. We employ for that the Unconventional minimal subtraction, recently proposed, and the Callan–Symanzik methods to probe the universality hypothesis by comparing the outcomes for the critical exponents evaluated in both methods and the ones calculated previously in massless theories renormalized at different renormalization schemes. Furthermore, the consistency of the former method is investigated for the first time in literature, to our knowledge. At the end, we compute the critical exponents at any loop level by an induction process and furnish the physical interpretation of the results.

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Exact Lorentz-violating q-deformed O(N) universality class

International Journal of Modern Physics D ◽

10.1142/s0218271819500500 ◽

2019 ◽

Vol 28 (03) ◽

pp. 1950050

Author(s):

P. R. S. Carvalho ◽

M. I. Sena-Junior

Keyword(s):

Critical Exponents ◽

Universality Class ◽

Field Theories ◽

Quantum Corrections ◽

Leading Order ◽

Loop Order ◽

Independent Field ◽

Group Methods ◽

Renormalization Group Methods ◽

Finite Loop

We examine the influence of exact Lorentz-violating symmetry mechanism on the radiative quantum corrections to the critical exponents for massless [Formula: see text]-deformed O([Formula: see text]) [Formula: see text] scalar field theories. For that, we employ three different and independent field-theoretic renormalization group methods for computing analytically the [Formula: see text]-deformed critical exponents up to next-to-leading order. Then, we generalize the former finite loop level results for any loop order. We show that the Lorentz-violating [Formula: see text]-deformed critical exponents, obtained through the three methods, turn out to be identical and furthermore the same as their Lorentz-invariant [Formula: see text]-deformed ones. We argue that this result is in accordance with the universality hypothesis.

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On the flat spacetime Galileons and the Born–Infeld type structures

International Journal of Modern Physics D ◽

10.1142/s0218271815500418 ◽

2015 ◽

Vol 24 (06) ◽

pp. 1550041

Author(s):

Cuauhtemoc Campuzano ◽

Rubén Cordero ◽

Miguel Cruz ◽

Efraín Rojas

Keyword(s):

Scalar Field ◽

Variational Analysis ◽

Momentum Density ◽

Type Structure ◽

Field Theories ◽

Flat Spacetime ◽

Arbitrary Dimensions ◽

Derivatives Of ◽

Galileon Field

We show how the flat spacetime Galileon field theories (FSGFT) in arbitrary dimensions can be obtained through a Born–Infeld (BI) type structure. This construction involves a brane metric and nonlinear combinations of derivatives of a scalar field. Our setup gives rise to some Galileon tensors and vectors useful for the variational analysis which are related to the momentum density of the probe Lovelock branes floating in a N-dimensional flat bulk. We find further that the Noether currents associated to these Galileon theories may be written in terms of such tensors.

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

International Journal of Modern Physics B ◽

10.1142/s0217979215502598 ◽

2016 ◽

Vol 30 (03) ◽

pp. 1550259 ◽

Cited By ~ 6

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.

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A note on one-loop soliton quantum mass corrections

Modern Physics Letters A ◽

10.1142/s0217732320501023 ◽

2020 ◽

Vol 35 (13) ◽

pp. 2050102

Author(s):

A. R. Aguirre ◽

G. Flores-Hidalgo

Keyword(s):

Scalar Field ◽

Field Theories ◽

Loop Order ◽

Regularization Scheme ◽

Alternative Derivation ◽

The One

We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1 + 1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its corresponding tadpole graph contribution and use the renormalization prescription that such added term vanishes with adequate counterterms. As a result, we get a finite unambiguous formula for the soliton quantum mass corrections up to one-loop order, which turns to be independent of the chosen regularization scheme.

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