scholarly journals Effective potential for a scalar field in three dimensions: Ising model in the ferromagnetic phase

1997 ◽  
Vol 55 (14) ◽  
pp. 8911-8917 ◽  
Author(s):  
M. M. Tsypin
Keyword(s):  
Scalar Field ◽  
Ising Model ◽  
Effective Potential ◽  
Three Dimensions ◽  
Ferromagnetic Phase

A NONPERTURBATIVE CALCULATION FOR THE EFFECTIVE POTENTIAL OF THE $\left(\frac{g}{4}\phi^{4}-J\phi\right)_{1+1}$ SCALAR FIELD THEORY USING THE OSCILLATOR REPRESENTATION METHOD WITH BOREL RESUMMATION

2007 ◽  
Vol 22 (06) ◽  
pp. 1265-1278
Author(s):  
ABOUZEID M. SHALABY ◽  
S. T. EL-BASYOUNY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Phase Transition ◽  
Scalar Field ◽  
External Magnetic Field ◽  
Effective Potential ◽  
Oscillator Representation ◽  
Constructive Field Theory ◽  
Representation Method ◽  
Oscillator Representation Method

We established a resummed formula for the effective potential of [Formula: see text] scalar field theory that can mimic the true effective potential not only at the critical region but also at any point in the coupling space. We first extend the effective potential from the oscillator representation method, perturbatively, up to g3 order. We supplement perturbations by the use of a resummation algorithm, originally due to Kleinert, Thoms and Janke, which has the privilege of using the strong coupling as well as the large coupling behaviors rather than the conventional resummation techniques which use only the large order behavior. Accordingly, although the perturbation series available is up to g3 order, we found a good agreement between our resummed effective potential and the well-known features from constructive field theory. The resummed effective potential agrees well with the constructive field theory results concerning existing and order of phase transition in the absence of an external magnetic field. In the presence of the external magnetic field, as in magnetic systems, the effective potential shows nonexistence of phase transition and gives the behavior of the vacuum condensate as a monotonic increasing function of J, in complete agreement with constructive field theory methods.

scholarly journals Noncommutative Friedmann equations in effective LQC

2020 ◽  
Vol 29 (06) ◽  
pp. 2050039
Author(s):  
Luis Rey Díaz-Barrón ◽  
Abraham Espinoza-García ◽  
S. Pérez-Payán ◽  
J. Socorro
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Quantum Cosmology ◽  
Equations Of Motion ◽  
Loop Quantum Cosmology ◽  
Friedmann Equations ◽  
Noncommutative Version ◽  
Previous Proposal ◽  
Free Scalar ◽  
Raychaudhuri Equations

In this work, we construct a noncommutative version of the Friedmann equations in the framework of effective loop quantum cosmology, extending and applying the ideas presented in a previous proposal by some of the authors. The model under consideration is a flat FRW spacetime with a free scalar field. First, noncommutativity in the momentum sector is introduced. We establish the noncommutative equations of motion and obtain the corresponding exact solutions. Such solutions indicate that the bounce is preserved, in particular, the energy density is the same as in the standard LQC. We also construct an extension of the modified Friedmann equations arising in effective LQC which incorporates corrections due to noncommutativity, and argue that an effective potential is induced. This, in turn, leads us to investigate the possibility of an inflationary era. Finally, we obtain the Friedmann and the Raychaudhuri equations when implementing noncommutativity in the configuration sector. In this case, no effective potential is induced.

scholarly journals General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1958
Author(s):  
Sabit Bekov ◽  
Kairat Myrzakulov ◽  
Ratbay Myrzakulov ◽  
Diego Sáez-Chillón Gómez
Keyword(s):  
Scalar Field ◽  
Simple Model ◽  
Spectral Index ◽  
Effective Potential ◽  
Modified Gravity ◽  
Palatini Formalism ◽  
Slow Roll ◽  
Slow Roll Inflation

Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model.

scholarly journals Quintessence in low-energy effective theory

2018 ◽  
Vol 168 ◽  
pp. 08004
Author(s):  
Tae Hoon Lee
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Cosmological Solution ◽  
Low Energy ◽  
Effective Theory ◽  
Late Time ◽  
Inverse Power Law ◽  
Virtual Interactions ◽  
The Universe ◽  
Gravitational Equations

Considering a theory of Brans-Dicke gravity with general couplings of a heavy field, we derive the low-energy effective theory action in the universe of temperature much lower than the heavy field mass. Gravitational equations and the Brans-Dicke scalar field equation including an effective potential of the scalar field are obtained, which is induced through virtual interactions of the heavy field in the late-time universe. We find a deSitter cosmological solution stemming from the inverse power law effective potential of the scalar field and discuss the possibility that the late time acceleration of our universe can be described by means of the solution.

ASYMPTOTIC QUASINORMAL MODES IN EINSTEIN–GAUSS–BONNET GRAVITY

2011 ◽  
Vol 26 (16) ◽  
pp. 2783-2794 ◽  
Author(s):  
J. SADEGHI ◽  
A. BANIJAMALI ◽  
M. R. SETARE ◽  
H. VAEZ
Keyword(s):  
Scalar Field ◽  
Effective Potential ◽  
Quasinormal Modes ◽  
Space Time ◽  
Massive Scalar ◽  
Massive Scalar Field ◽  
Momentum Vector ◽  
Five Dimensions ◽  
Bonnet Gravity ◽  
Temperature Scalar

In this paper we consider a massive scalar field on the boundary of AdS space–time and calculate the quasinormal modes for the string inspired Einstein–Gauss–Bonnet gravity in five dimensions. We study the effects of Gauss–Bonnet parameter, temperature, scalar field's mass and momentum vector on the effective potential and quasinormal modes.

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