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.

scholarly journals Two interacting scalars system in curved spacetime — vacuum stability from the curved spacetime Effective Field Theory (cEFT) perspective

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Zygmunt Lalak ◽  
Anna Nakonieczna ◽  
Łukasz Nakonieczny
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Field Potential ◽  
Scalar Fields ◽  
Effective Field ◽  
Kinetic Term ◽  
Curved Spacetime ◽  
Minimal Coupling ◽  
Vacuum Stability ◽  
Higher Dimensional

Abstract In this article we investigated the influence of the gravity mediated higher dimensional operators on the issue of vacuum stability in a model containing two interacting scalar fields. As a framework we used the curved spacetime Effective Field Theory (cEFT) applied to the aforementioned system in which one of the scalars is heavy. After integrating out the heavy scalar we used the standard Euclidean approach to the obtained cEFT. Apart from analyzing the influence of standard operators like the non-minimal coupling to gravity and the dimension six contribution to the scalar field potential, we also investigated the rarely discussed dimension six contribution to the kinetic term and the new gravity mediated contribution to the scalar quartic self-interaction.

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.

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.

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.

scholarly journals SPECTRAL GEOMETRY AND CAUSALITY

1998 ◽  
Vol 13 (15) ◽  
pp. 2693-2708 ◽  
Author(s):  
TOMÁŠ KOPF
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Spectral Data ◽  
Physical Interpretation ◽  
Lorentzian Manifold ◽  
Space Time ◽  
Effective Field ◽  
Spectral Geometry ◽  
Causal Relationships ◽  
Classical Space

For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical space–time, at least approximately. However, quantum gravity may eventually provide classical space–times by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a space–time manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.

scholarly journals SOME ALGEBRAIC SYMMETRIES OF (2, 2)-SUPERSYMMETRIC SYSTEMS

2001 ◽  
Vol 16 (10) ◽  
pp. 663-671
Author(s):  
TRISTAN HÜBSCH
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hilbert Spaces ◽  
Dimensional Space ◽  
Space Time ◽  
Effective Field ◽  
Target Space ◽  
Two Dimensional ◽  
Target Field ◽  
Dimensional Space Time

The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2, 2)-supersymmetric systems in two-dimensional space–time which are closely related to superstring models. They all turn out to possess some hitherto unexploited and geometrically and topologically unobstructed symmetries, providing new tools for studying the topology and geometry of superstring target space–times, and so the dynamics of the effective field theory in these.

scholarly journals TIME AND TACHYON

2003 ◽  
Vol 18 (26) ◽  
pp. 4869-4888 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Recent Analysis ◽  
Late Time ◽  
Classical Dynamics ◽  
One To One ◽  
Definition Of

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity.

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