The Lattice Fermion Problem and Weak Coupling Perturbation Theory

1980 ◽  
pp. 235-247
Author(s):  
Luuk H. Karsten
Keyword(s):  
Perturbation Theory ◽  
Weak Coupling ◽  
Lattice Fermion

scholarly journals Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

Aspects of the weak-coupling theory of open systems

1983 ◽  
Vol 61 (11) ◽  
pp. 1479-1485 ◽  
Author(s):  
I. D. Cox ◽  
W. E. Hagston ◽  
B. J. Holmes
Keyword(s):  
Perturbation Theory ◽  
Open System ◽  
Weak Coupling ◽  
Open Systems ◽  
Higher Order ◽  
Projection Operators ◽  
Coupling Theory ◽  
Weak Coupling Theory ◽  
Damping Theory ◽  
Insight Into

Damping theory of an open system S is usually formulated in terms of projection operators which introduce nonuniqueness into the analysis. An insight into the nature of the approximations that arise from this aspect of the formalism is revealed by considering systems of varying complexity. This leads to the conclusion that the results of higher order perturbation theory approximations may not be meaningful.

scholarly journals Phases of a strongly coupled four-fermion theory

2018 ◽  
Vol 175 ◽  
pp. 03004 ◽  
Author(s):  
David Schaich ◽  
Simon Catterall
Keyword(s):  
Strong Coupling ◽  
Weak Coupling ◽  
Strongly Coupled ◽  
Coupling Phase ◽  
Long Range Correlations ◽  
Mass Gap ◽  
Narrow Region ◽  
Lattice Field ◽  
Lattice Symmetry ◽  
Lattice Fermion

We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant fourfermion interaction. As in previous studies of four-fermion and Higgs–Yukawa models with different lattice fermion discretizations, we observe a strong-coupling phase in which the system develops a mass gap without breaking any lattice symmetry. This symmetric strong-coupling phase is separated from the symmetric weak-coupling phase by a narrow region of four-fermi coupling in which the system exhibits long-range correlations.

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.

Weak coupling perturbation theory by Langevin dynamics: Fourth loop and beyond

1995 ◽  
Vol 42 (1-3) ◽  
pp. 867-869 ◽  
Author(s):  
F. Di Renzo ◽  
G. Marchesini ◽  
P. Marenzoni ◽  
E. Onofri
Keyword(s):  
Perturbation Theory ◽  
Weak Coupling ◽  
Langevin Dynamics

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.

POLARON IN THE SINGLE-WALLED POLAR NANOTUBE

2006 ◽  
Vol 20 (27) ◽  
pp. 1771-1776 ◽  
Author(s):  
N. M. GUSEINOV ◽  
O. Z. ALEKPEROV ◽  
S. S. GUSEINOVA
Keyword(s):  
Perturbation Theory ◽  
Cylindrical Surface ◽  
Weak Coupling ◽  
Electron Gas ◽  
Energy Shift ◽  
Longitudinal Optical ◽  
Two Dimensional ◽  
Polar Material ◽  
Bulk Phonon ◽  
Polaron Energy

The model of electron gas situated on the two-dimensional continual cylindrical surface is suggested to describe a polaron in the single-walled nanotube made of polar material. The problem on weak-coupling polaron is solved using perturbation theory. Analytical expression for the polaron energy shift of the subband is found in the case of bulk phonon approximation and the case when longitudinal optical (LO) phonons are confined on the cylinder's surface. It is shown that in the second case the polaron effect is negligible.

scholarly journals WAVY WILSON LINE AND AdS/CFT

2005 ◽  
Vol 20 (13) ◽  
pp. 2833-2846 ◽  
Author(s):  
GORDON W. SEMENOFF ◽  
DONOVAN YOUNG
Keyword(s):  
Perturbation Theory ◽  
Weak Coupling ◽  
Functional Form ◽  
Wilson Line ◽  
Leading Order ◽  
Small Deviations ◽  
Loop Equation ◽  
Hooft Coupling ◽  
Straight Line ◽  
Wavy Line

Wilson loops which are small deviations from straight, infinite lines, called wavy lines, are considered in the context of the AdS/CFT correspondence. A single wavy line and the connected correlation function of a straight and wavy line are considered. It is argued that, to leading order in "waviness," the functional form of the loop is universal and the coefficient, which is a function of the 't Hooft coupling, is found in weak coupling perturbation theory and the strong coupling limit using the AdS/CFT correspondence. Supersymmetric arguments are used to simplify the computation and to show that the straight line obeys the Migdal–Makeenko loop equation.

scholarly journals DIMENSIONAL CONTINUATION WITHOUT PERTURBATION THEORY

1995 ◽  
Vol 10 (17) ◽  
pp. 1195-1199
Author(s):  
VIPUL PERIWAL
Keyword(s):  
Perturbation Theory ◽  
Strong Coupling ◽  
Correlation Functions ◽  
Weak Coupling ◽  
Strong Coupling Expansion ◽  
Weighted Sums ◽  
Arbitrary Integer ◽  
Correct Dimension

A formula is proposed for continuing physical correlation functions to noninteger numbers of dimensions, expressing them as infinite weighted sums over the same correlation functions in arbitrary integer dimensions. The formula is motivated by studying the strong coupling expansion, but the end result makes no reference to any perturbation theory. It is shown that the formula leads to the correct dimension dependence in weak coupling perturbation theory at one-loop.

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