scholarly journals Continued Functions and Perturbation Series: Simple Tools for Convergence of Diverging Series in O(n)-Symmetric $$\phi ^4$$ Field Theory at Weak Coupling Limit

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Venkat Abhignan ◽  
R. Sankaranarayanan
Keyword(s):  
Field Theory ◽  
Weak Coupling ◽  
Perturbation Series ◽  
Weak Coupling Limit

Reorganizing Finite Temperature Field Theory: Part I.: Scalar Field Theory

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1277-1280 ◽  
Author(s):  
Michael Strickland
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Temperature Field ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Finite Temperature Field Theory ◽  
Expansion Point ◽  
Perturbative Limit ◽  
Standard Perturbation Theory

I present a method for self-consistently including the effects of screening in finite-temperature field theory calculations. The method reproduces the perturbative limit in the weak-coupling limit and for intermediate couplings this method has much better convergence than standard perturbation theory. The method relies on a reorganization of perturbation theory accomplished by shifting the expansion point used to calculate quantum loop corrections. I will present results from a three-loop calculation within this formalism for scalar λϕ4.

ON A PHASE STRUCTURE OF A TWO-DIMENSIONAL (φ2)2 FIELD THEORY

1989 ◽  
Vol 04 (18) ◽  
pp. 4977-4990 ◽  
Author(s):  
G. V. EFIMOV
Keyword(s):  
Field Theory ◽  
Phase Transitions ◽  
Phase Structure ◽  
Weak Coupling ◽  
Scalar Fields ◽  
Perturbation Series ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Effective Coupling ◽  
Two Phases

Two models of scalar fields with the interaction Lagrangians gφ4 and [Formula: see text] are considered in ℝ2. There are phase transitions in these models for a certain g = gc. It is shown that the spontaneous symmetry breaking takes place for g > gc. The description of the two phases for g < gc and g > gc is given. The effective coupling constants in perturbation series are less than unity for both the phases so that these models describe the systems with weak coupling. In the second model the "Goldstone" particles have nonzero masses in the phase g > gc.

CONVERGENT WEAK COUPLING EXPANSIONS FOR LATTICE FIELD THEORIES THAT LOOK LIKE PERTURBATION SERIES

1989 ◽  
Vol 01 (01) ◽  
pp. 47-87 ◽  
Author(s):  
GERHARD MACK ◽  
ANDREAS PORDT
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Weak Coupling ◽  
Free Field ◽  
Perturbation Series ◽  
Field Theories ◽  
Lattice Field Theory ◽  
Lattice Field ◽  
Local Coupling ◽  
New Form

We propose a new form of convergent weak coupling expansion for the lattice field theory. It has the advantage that it is very similar to standard (Feynman) perturbation theory. Convergence is proven for sufficiently weak local coupling, i.e. when the theory is close to a free field theory. In the proof, use of analyticity in field variables, as pioneered by Kupiainen and Gawedzki, is supplemented with techniques for handling derivatives with respect to free propagators.

scholarly journals An obstacle to sub-AdS holography for SYK-like models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang ◽  
Yingfei Gu ◽  
Alexei Kitaev
Keyword(s):  
Lyapunov Exponent ◽  
Weak Coupling ◽  
Kinetic Coefficient ◽  
Weak Coupling Limit ◽  
Branching Time ◽  
Quasiparticle Lifetime

Abstract We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

ENERGY BAND OVERLAPPING IN HIGH-Tc SUPERCONDUCTORS

1996 ◽  
Vol 10 (30) ◽  
pp. 1483-1490 ◽  
Author(s):  
M. MORENO ◽  
R. M. MÉNDEZ-MORENO ◽  
M. A. ORTIZ ◽  
S. OROZCO
Keyword(s):  
Weak Coupling ◽  
Cuprate Superconductors ◽  
Weak Coupling Limit ◽  
Band Model ◽  
Coupling Constant ◽  
High Tc Superconductors ◽  
Energy Bands ◽  
Effective Coupling ◽  
High Tc ◽  
Two Band Model

Multi-band superconductors are analyzed and the relevance of overlapping energy bands to the high-T c of these materials is studied. Within the BCS framework, a two band model with generalized Fermi surface topologies is developed. Values of the overlapped occupancy parameters for typical cuprate superconductors are obtained as a function of the ratio R and the effective coupling constant, λ, in the weak-coupling limit. The overlap scale is of the order or lower than the cutoff (Debye) energy. The typical behavior of the isotope effect is obtained. As these superconductors have transition temperatures above the phonon barrier, the results of this approach are important to the generic understanding of the high-T c superconducting mechanism.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

scholarly journals Continued functions and perturbation series: Simple tools for convergence of diverging series in $O(n)$-symmetric $\phi^4$ field theory at weak coupling limit

2021 ◽  
Author(s):  
Venkat Abhignan ◽  
Sankaranarayanan R.
Keyword(s):  
Field Theory ◽  
Continuous Phase ◽  
Perturbation Series ◽  
Experimental Result ◽  
Unknown Parameters ◽  
Epsilon Expansion ◽  
Theoretical Predictions ◽  
Lambda Point ◽  
Different Dimensions ◽  
Dimensions Of Space

Abstract We determine universal critical exponents that describe the continuous phase transitions in different dimensions of space. We use continued functions without any external unknown parameters to obtain analytic continuation for the recently derived 7-loop $\epsilon$ expansion from $O(n)$-symmetric $\phi^4$ field theory. Employing a new blended continued function, we obtain critical exponent $\alpha=-0.01211$ for the phase transition of superfluid helium which matches closely with the most accurate experimental value. This result addresses the long-standing discrepancy between the theoretical predictions and precise experimental result of $O(2)$ $\phi^4$ model known as "$\lambda$-point specific heat experimental anomaly". Further we have also examined the applicability of such continued functions in other examples of field theories.

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