Dependence on the renormalization points in a simple scalar theory

1982 ◽  
Vol 60 (6) ◽  
pp. 789-792
Author(s):  
Gerry McKeon
Keyword(s):  
Scalar Potential ◽  
Scalar Fields ◽  
Simple Theory ◽  
Coupling Constants ◽  
Scalar Theory

One loop corrections to the scalar potential in a simple theory involving two scalar fields [Formula: see text] and ψ are evaluated. The dependence of the renormalized coupling constants on the renormalization points [Formula: see text] and ψ0 are examined. It is found that under the change [Formula: see text], ψ0 → (1 + ε)ψ0, the coupling constants vary according to a set of equations that are independent of the ratio [Formula: see text]. It is shown that the coupling constants are not altered if [Formula: see text] is changed.

scholarly journals Renormalization and radiative corrections to masses in a general Yukawa model

2018 ◽  
Vol 33 (03) ◽  
pp. 1850019 ◽  
Author(s):  
M. Fox ◽  
W. Grimus ◽  
M. Löschner
Keyword(s):  
Scalar Potential ◽  
Vacuum Expectation ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Tree Level ◽  
Majorana Fermion ◽  
Dirac Fermions ◽  
Yukawa Couplings ◽  
Fermion Fields ◽  
The Masses

We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields [Formula: see text], general Yukawa couplings and a [Formula: see text] symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the [Formula: see text] symmetry by vacuum expectation values (VEVs) of the [Formula: see text]. Introducing the shifted fields [Formula: see text] whose VEVs vanish, [Formula: see text] renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the [Formula: see text]. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals Effective Scalar Potential in Asymptotically Safe Quantum Gravity

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 45
Author(s):  
Christof Wetterich
Keyword(s):  
Quantum Gravity ◽  
Top Quark ◽  
Particle Physics ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Standard Model ◽  
Scaling Potential ◽  
Realistic Description ◽  
The Masses ◽  
Dynamical Dark Energy

We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic safety. Scaling solutions with vanishing relevant parameters can be sufficient for a realistic description of particle physics and cosmology, leading to an asymptotically vanishing “cosmological constant” or dynamical dark energy.

scholarly journals ON THE QUANTUM CHROMODYNAMICS OF A MASSIVE VECTOR FIELD IN THE ADJOINT REPRESENTATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350054 ◽  
Author(s):  
ALFONSO R. ZERWEKH
Keyword(s):  
Vector Field ◽  
Quantum Chromodynamics ◽  
Extra Dimensions ◽  
Scalar Fields ◽  
Discrete Symmetry ◽  
Adjoint Representation ◽  
Coupling Constants ◽  
Gauge Symmetries ◽  
Gauge Fixing ◽  
Definition Of

In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that gauge invariance is not enough to constraint the couplings. Nevertheless, the requirement of unitarity fixes the values of the coupling constants, which otherwise would be arbitrary. Additionally, it opens a new discrete symmetry which makes the coloron stable and avoid its resonant production at a collider. On the other hand, a judicious definition of the gauge fixing terms modifies the propagator of the massive field making it well-behaved in the ultraviolet limit. The relation between our model and the more general approach based on extended gauge symmetries is also discussed.

scholarly journals Interface junctions in QCD${}_4$

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Pranay Gorantla ◽  
Ho Tat Lam
Keyword(s):  
Effective Field Theories ◽  
Quantum Chromodynamics ◽  
Effective Field ◽  
Low Energy ◽  
Coupling Constants ◽  
Field Theories ◽  
Scalar Theory ◽  
Complex Mass ◽  
Spatially Varying ◽  
Chern Simons

We study 3+1 dimensional SU(N)SU(N) Quantum Chromodynamics (QCD) with N_fNf degenerate quarks that have a spatially varying complex mass. It leads to a network of interfaces connected by interface junctions. We use anomaly inflow to constrain these defects. Based on the chiral Lagrangian and the conjectures on the interfaces, characterized by a spatially varying \thetaθ-parameter, we propose a low-energy description of such networks of interfaces. Interestingly, we observe that the operators in the effective field theories on the junctions can carry baryon charges, and their spin and isospin representations coincide with baryons. We also study defects, characterized by spatially varying coupling constants, in 2+1 dimensional Chern-Simons-matter theories and in a 3+1 dimensional real scalar theory.

INTERACTING GENERALIZED DARK ENERGY AND RECONSTRUCTION OF SCALAR FIELD MODELS

2013 ◽  
Vol 28 (38) ◽  
pp. 1350180 ◽  
Author(s):  
M. SHARIF ◽  
ABDUL JAWAD
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Dark Energy Model ◽  
Cold Dark Matter ◽  
Scalar Potential ◽  
Scalar Fields ◽  
Phantom Divide ◽  
Evolution Parameter ◽  
Scalar Field Models ◽  
Phantom Divide Line

In this paper, we consider the interacting generalized dark energy with cold dark matter and analyze the behavior of evolution parameter via dark energy and interacting parameters. It is found that the evolution parameter crosses the phantom divide line in most of the cases of integration constants. We also establish the correspondence of scalar field models (quintessence, k-essence and dilaton) with this dark energy model in which scalar fields show the increasing behavior. The scalar potential corresponds to attractor solutions in quintessence case.

Stability of renormalization group fixed points and decay of correlations

2019 ◽  
pp. 101-110
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gradient Flow ◽  
Scalar Fields ◽  
Effective Field ◽  
Coupling Constants ◽  
Critical Systems ◽  
Universal Properties ◽  
General Physical

Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.

scholarly journals The Ambiguity in the Definition and Behavior of the Gravitational and Cosmological `Coupling Constants’ in the Theory of Induced Gravity

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 81 ◽  
Author(s):  
Farkhat Zaripov
Keyword(s):  
Gravitational Interaction ◽  
Scalar Fields ◽  
Coupling Constants ◽  
De Sitter ◽  
Induced Gravity ◽  
Mean Values ◽  
Gravitational And Cosmological Constants ◽  
Centrally Symmetric ◽  
Walker Metric ◽  
Cosmological Constants

This work is the extension of author`s research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS). We consider equations with quadratic potential that are symmetric with respect to scale transformations. The solutions of the equations obtained for the case of spaces defined by the Friedman-Robertson-Walker metric, as well as for a centrally symmetric space are investigated. In our model arise effective gravitational and cosmological “constants”, which are defined by the “mean square” of the scalar fields. In obtained solutions the values of such parameters as “Hubble parameter”, gravitational and cosmological “constants” in the RS stage fluctuate near monotonically evolving mean values. These parameters are matched with observational data, described as phenomena of dark energy and dark matter. The MTIG equations for the case of a centrally symmetric gravitational field, in addition to the Schwarzschild-de Sitter solutions, contain solutions that lead to the new physical effects at large distances from the center. The Schwarzschild-Sitter solution becomes unstable and enters the oscillatory regime. For distances greater than a certain critical value, the following effects can appear: deviation from General relativity and Newton’s law of gravitational interaction, antigravity.

SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME

2013 ◽  
Vol 28 (31) ◽  
pp. 1350137 ◽  
Author(s):  
GEUSA DE A. MARQUES ◽  
V. B. BEZERRA ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Cosmic String ◽  
Relativistic Particle ◽  
Energy Levels ◽  
Scalar Potential ◽  
Scalar Fields ◽  
The Self ◽  
Dependent Mass ◽  
Scalar Potentials ◽  
Position Dependent Mass

We consider the problem of a relativistic particle with position-dependent mass in the presence of a Coulomb and a scalar potentials in the background spacetime generated by a cosmic string. The scalar potential arises from the self-interaction potential which is induced by the conical geometry of the spacetime under consideration. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle. The behavior of the energy levels on the parameters associated with the presence of the cosmic string and with the fact that the mass of the particle depends on its position is also analyzed.

scholarly journals SOME ASPECTS OF SPHERICAL SYMMETRIC EXTREMAL DYONIC BLACK HOLES IN 4D N = 1 SUPERGRAVITY

2013 ◽  
Vol 28 (18) ◽  
pp. 1350084 ◽  
Author(s):  
BOBBY E. GUNARA ◽  
FREDDY P. ZEN ◽  
FIKI T. AKBAR ◽  
AGUS SUROSO ◽  
ARIANTO
Keyword(s):  
Black Hole ◽  
Scalar Potential ◽  
Local Existence ◽  
Scalar Fields ◽  
Asymptotic Region ◽  
De Sitter ◽  
Complex Scalar ◽  
Symmetric Black Hole ◽  
Scalar Potentials ◽  
Nonzero Scalar

In this paper, we study several aspects of extremal spherical symmetric black hole solutions of four-dimensional N = 1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region, the complex scalars are fixed and regular which can be viewed as the critical points of the black hole and the scalar potentials with vanishing scalar charges. It follows that the asymptotic geometries are of a constant and nonzero scalar curvature which are generally not Einstein. These spaces could also correspond to the near horizon geometries which are the product spaces of a two anti-de Sitter surface and the two sphere if the value of the scalars in both regions coincide. In addition, we prove the local existence of nontrivial radius dependent complex scalar fields which interpolate between the horizon and the asymptotic region. We finally give some simple ℂn-models with both linear superpotential and gauge couplings.

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