scholarly journals Perturbative expansion around the Gaussian effective potential of the fermion field theory

1998 ◽  
Vol 58 (12) ◽  
Author(s):  
Geon Hyoung Lee ◽  
Tack Hwi Lee ◽  
Jae Hyung Yee
Keyword(s):  
Field Theory ◽  
Effective Potential ◽  
Perturbative Expansion ◽  
Fermion Field ◽  
Gaussian Effective Potential

THE UNCERTAINTY OF THE GAUSSIAN EFFECTIVE POTENTIAL

1988 ◽  
Vol 03 (09) ◽  
pp. 2143-2163 ◽  
Author(s):  
R. MUÑOZ-TAPIA ◽  
J. TARON ◽  
R. TARRACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Effective Potential ◽  
Anharmonic Oscillator ◽  
Liouville Theory ◽  
Quantum Field ◽  
First Case ◽  
Gaussian Effective Potential

An uncertainty is introduced for the Gaussian Effective Potential. The definition is quite straightforward for quantum mechanics but fairly subtle for quantum field theory. The uncertainty provides a good estimation of the error in the first case, but renormalization seems to spoil its usefulness in the second case. The examples considered are the anharmonic oscillator, λϕ4 in 3+1 dimensions and the Liouville theory in 1+1 dimensions.

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.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

scholarly journals O(N)-symmetric λφ4theory: The Gaussian-effective-potential approach

1987 ◽  
Vol 35 (8) ◽  
pp. 2407-2414 ◽  
Author(s):  
P. M. Stevenson ◽  
B. Allès ◽  
R. Tarrach
Keyword(s):  
Effective Potential ◽  
Potential Approach ◽  
Gaussian Effective Potential

Gaussian Approach to (1 + 1) Dimensional φ6 Solitons at Finite Temperature

1990 ◽  
Vol 45 (6) ◽  
pp. 779-782
Author(s):  
Rajkumar Roychoudhury ◽  
Manasi Sengupta
Keyword(s):  
Critical Temperature ◽  
Effective Potential ◽  
Finite Temperature ◽  
Soliton Solutions ◽  
Gap Equation ◽  
Potential Approach ◽  
Mass Gap ◽  
Gaussian Effective Potential

AbstractUsing the Gaussian effective potential approach, φ6 soliton solutions at finite temperature are studied for both the general case and the particular case λ2 = 2ξm2. A critical temperature is found at which soliton solutions cease to exist. The effective potential together with the mass-gap equation are studied in detail, and comparison with existing work on this subject is made

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