ON THE VACUUM STABILITY IN THE SUPERRENORMALIZED YUKAWA-TYPE THEORY

1990 ◽  
Vol 05 (03) ◽  
pp. 531-541
Author(s):  
G.V. EFIMOV ◽  
G. GANBOLD
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Effective Potential ◽  
Ground State ◽  
Type Theory ◽  
Critical Value ◽  
Coupling Constant ◽  
Vacuum Stability ◽  
Expectation Value ◽  
The Stability

The stability of the ground state and the possibility of the appearance of a phase transition in the superrenormalizable nonlocal Yukawa-type field theory are investigated. A variational estimation of the upper bound for the effective potential is obtained. It is shown that there exists a finite critical value for the boson-fermion coupling constant. The initial vacuum becomes unstable when this coupling constant exceeds the critical value. As a result, the system under consideration goes into the phase with nonvanishing expectation value of the field.

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 Spin(p + 1, p + 1) COVARIANT Dp-BRANE BOUND STATES

2001 ◽  
Vol 16 (17) ◽  
pp. 3025-3040 ◽  
Author(s):  
P. SUNDELL
Keyword(s):  
Field Theory ◽  
Ground State ◽  
Bound States ◽  
Type Ii ◽  
Duality Group ◽  
Zero Force ◽  
Force Condition ◽  
The Stability

We construct Spin (p + 1, p + 1) covariant D p-brane bound states by using the fact that the potentials in the RR sector of toroidically compactified type II supergravity transform as a chiral spinor of the T duality group. As an application, we show the invariance of the zero-force condition for a probe D-brane under noncommutative deformations of the background, which gives a holographic proof of the stability of the corresponding field theory ground state under noncommutative deformations. We also identify the Spin (p + 1, p + 1) transformation laws by examining the covariance of the D-brane Lagrangians.

PHASE TRANSITION IN $g\varphi^4_2$ THEORY

1992 ◽  
Vol 07 (24) ◽  
pp. 2189-2197 ◽  
Author(s):  
G. V. EFIMOV ◽  
G. GANBOLD
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Effective Potential ◽  
Variational Approach ◽  
Two Dimensions ◽  
Second Order ◽  
Complete Agreement ◽  
Vacuum Stability ◽  
Second Order Phase Transition

The vacuum stability of a scalar gφ4 theory in two dimensions is studied. A variational approach is applied to estimate the effective potential in this model. We find that the second order phase transition takes place. It is in complete agreement with the Simon-Griffiths theorem.

scholarly journals A Solvable Twisted One-Plaquette Model

1997 ◽  
Vol 12 (15) ◽  
pp. 2741-2762 ◽  
Author(s):  
M. Billó ◽  
A. D'Adda
Keyword(s):  
Phase Transition ◽  
Heat Kernel ◽  
Quantum Fluctuations ◽  
Critical Value ◽  
Classical Solutions ◽  
Coupling Constant ◽  
Time Direction ◽  
Distribution Of Eigenvalues ◽  
Kernel Model ◽  
Link Variable

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the timelike link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the Hamiltonian limit, and the related Douglas–Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, and compare it to previous results by Karsch.

COLOR CONFINEMENT AND FINITE TEMPERATURE QCD PHASE TRANSITION

2004 ◽  
Vol 19 (02) ◽  
pp. 271-285 ◽  
Author(s):  
H. C. PANDEY ◽  
H. C. CHANDOLA ◽  
H. DEHNEN
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Effective Potential ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Expectation Value ◽  
Qcd Phase Transition ◽  
Qcd Vacuum ◽  
Color Confinement

We study an effective theory of QCD in which the fundamental variables are dual magnetic potentials coupled to the monopole field. Dual dynamics are then used to explain the properties of QCD vacuum at zero temperature as well as at finite temperatures. At zero temperature, the color confinement is realized through the dynamical breaking of magnetic symmetry, which leads to the magnetic condensation of QCD vacuum. The flux tube structure of SU(2) QCD vacuum is investigated by solving the field equations in the low energy regimes of the theory, which guarantees dual superconducting nature of the QCD vacuum. The QCD phase transition at finite temperature is studied by the functional diagrammatic evaluation of the effective potential on the one-loop level. We then obtained analytical expressions for the vacuum expectation value of the condensed monopoles as well as the masses of glueballs from the temperature dependent effective potential. These nonperturbative parameters are also evaluated numerically and used to determine the critical temperature of the QCD phase transition. Finally, it is shown that near the critical temperature (Tc≃0.195 GeV ), continuous reduction of vacuum expectation value (VEV) of the condensed monopoles caused the disappearance of vector and scalar glueball masses, which brings a second order phase transition in pure SU(2) gauge QCD.

scholarly journals MATRIX MODEL APPROACH TO d>2 NONCRITICAL SUPERSTRINGS

1995 ◽  
Vol 10 (34) ◽  
pp. 2639-2649 ◽  
Author(s):  
AKIKAZU HASHIMOTO ◽  
IGOR R. KLEBANOV
Keyword(s):  
Field Theory ◽  
Matrix Model ◽  
Light Cone ◽  
Critical Value ◽  
Coupling Constant ◽  
Numerical Evidence ◽  
Large N ◽  
Light Cone Quantization ◽  
Model Approach

We apply light-cone quantization to a (1+1)-dimensional supersymmetric field theory of large-N matrices. We provide some preliminary numerical evidence that when the coupling constant is tuned to a critical value, this model describes a (2+1)-dimensional noncritical superstring.

DEFECT THEORY OF SOLID–LIQUID TRANSITION AND INTERFACE

1993 ◽  
Vol 07 (21) ◽  
pp. 1373-1381
Author(s):  
A. FERRAZ
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Surface Tension ◽  
Theory Model ◽  
Planar Interface ◽  
Elastic Continuum ◽  
First Order ◽  
Liquid Transition ◽  
The Stability ◽  
Solid Liquid

In this work, we develop a field theory model for the solid–liquid transition and planar interface induced by dislocation lines in an elastic continuum. We show that the phase transition which emerges from our model is of first order kind. We calculate the interface solution, the surface tension and, finally, we end up discussing the stability of the field solutions.

scholarly journals VACUUM STABILITY OF THE ${\mathcal{PT}}$-SYMMETRIC (-ϕ4) SCALAR FIELD THEORY

2013 ◽  
Vol 28 (08) ◽  
pp. 1350023 ◽  
Author(s):  
ABOUZEID M. SHALABY
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Canonical Quantization ◽  
Field Potential ◽  
Space Time ◽  
Effective Field ◽  
Vacuum Stability ◽  
Metric Operator ◽  
Equal Time Commutation

In this paper, we study the vacuum stability of the classical unstable (-ϕ4) scalar field potential. Regarding this, we obtained the effective potential, up to second-order in the coupling, for the theory in 1+1 and 2+1 space–time dimensions. We found that the obtained effective potential is bounded-from-below, which proves the vacuum stability of the theory in space–time dimensions higher than the previously studied 0+1 case. In our calculations, we used the canonical quantization regime in which one deals with operators rather than classical functions used in the path integral formulation. Therefore, the non-Hermiticity of the effective field theory is obvious. Moreover, the method we employ implements the canonical equal-time commutation relations and the Heisenberg picture for the operators. Thus, the metric operator is implemented in the calculations of the transition amplitudes. Accordingly, the method avoids the very complicated calculations needed in other methods for the metric operator. To test the accuracy of our results, we obtained the exponential behavior of the vacuum condensate for small coupling values, which has been obtained in the literature using other methods. We assert that this work is interesting, as all the studies in the literature advocate the stability of the (-ϕ4) theory at the quantum mechanical level while our work extends the argument to the level of field quantization.

Sign in / Sign up

Export Citation Format

Share Document