Effective-Action Expansion in Perturbation Theory

1985 ◽  
Vol 54 (12) ◽  
pp. 1222-1225 ◽  
Author(s):  
Lai-Him Chan
Keyword(s):  
Perturbation Theory ◽  
Effective Action

scholarly journals The Leutwyler–Smilga relation on the lattice

2019 ◽  
Vol 35 (01) ◽  
pp. 1950346 ◽  
Author(s):  
Gernot Münster ◽  
Raimar Wulkenhaar
Keyword(s):  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Effective Action ◽  
Lattice Spacing ◽  
Chiral Perturbation ◽  
Quark Masses

According to the Leutwyler–Smilga relation, in Quantum Chromodynamics (QCD), the topological susceptibility vanishes linearly with the quark masses. Calculations of the topological susceptibility in the context of lattice QCD, extrapolated to zero quark masses, show a remnant nonzero value as a lattice artefact. Employing the Atiyah–Singer theorem in the framework of Symanzik’s effective action and chiral perturbation theory, we show the validity of the Leutwyler–Smilga relation in lattice QCD with lattice artefacts of order a2 in the lattice spacing a.

scholarly journals LAGRANGIAN Sp(3) BRST SYMMETRY FOR IRREDUCIBLE GAUGE THEORIES

2001 ◽  
Vol 16 (17) ◽  
pp. 2975-3009 ◽  
Author(s):  
C. BIZDADEA ◽  
S. O. SALIU
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Gauge Fixing ◽  
Homological Perturbation Theory ◽  
Canonical Generator ◽  
Homological Perturbation

The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket–antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.

scholarly journals Singular structure of the QED effective action

2019 ◽  
Vol 49 ◽  
pp. 1960006
Author(s):  
B. A. Fayzullaev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Singular Perturbation ◽  
Effective Action ◽  
Electromagnetic Interaction ◽  
Perturbation Series ◽  
Singular Perturbation Theory ◽  
Quantum Field ◽  
Coupling Constant

The equations for the QED effective action derived in Ref. 3 are considered using singular perturbation theory. The effective action is divided into regular and singular (in coupling constant) parts. It is shown that expression for the regular part coincides with usual Feynman perturbation series over coupling constant, while the remainder has essential singularity at the vanishing coupling constant: [Formula: see text]. This means that in the frame of quantum field theory it is impossible “to switch off” electromagnetic interaction in general and pass on to “free electron”.

EQUIVALENCE OF LIOUVILLE THEORY AND 2-D QUANTUM GRAVITY

1991 ◽  
Vol 06 (09) ◽  
pp. 745-767 ◽  
Author(s):  
ERIC D’HOKER
Keyword(s):  
Perturbation Theory ◽  
Invariant Measure ◽  
Quantum Gravity ◽  
Effective Potential ◽  
Effective Action ◽  
Liouville Theory ◽  
Ward Identities ◽  
Explicit Equation ◽  
Translation Invariant

The equivalence of 2-dimensional quantum gravity and Liouville theory quantized with the standard translation invariant measure, is shown to hold to all orders in perturbation theory. Also, an explicit equation for the Liouville effective action as a function of the effective potential is derived from Weyl Ward identities. We speculate on some of the non-perturbative aspects of the theory.

scholarly journals Curvature Expansion for the Gluodynamics String Including Perturbative Gluonic Contributions

1997 ◽  
Vol 12 (27) ◽  
pp. 2047-2056 ◽  
Author(s):  
D. V. Antonov ◽  
D. Ebert
Keyword(s):  
Perturbation Theory ◽  
Path Integral ◽  
Effective Action ◽  
Wilson Loop ◽  
Color Space ◽  
String Tension ◽  
Coupling Constant ◽  
Qcd Vacuum ◽  
Nonperturbative Qcd ◽  
String Worldsheet

Perturbation theory, which represents a Wilson loop in the SU(2) gluodynamics as an integral over all the orientations in color space, in the nonperturbative QCD vacuum and the non-Abelian Stokes theorem is applied to a derivation of the correction to the string effective action in the lowest order in the coupling constant g. This correction is due to the interaction of perturbative gluons with the string worldsheet and affects only the coupling constant of the rigidity term, while its contribution to the string tension of the Nambu–Goto term vanishes. The obtained correction to the rigidity coupling constant multiplicatively depends on the color "spin" of the representation of the Wilson loop under consideration and a certain path integral, which includes the background Wilson loop average.

Perturbation theory

2021 ◽  
pp. 147-170
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Momentum Space ◽  
Feynman Diagrams ◽  
Green Functions ◽  
General Description ◽  
Loop Expansion

This chapter provides a general description of perturbation theory in terms of Feynman diagrams. The general prescriptions of constructing Feynman diagrams in momentum space are given, including for an S-matrix. The connected Green functions and the corresponding generation functional are defined with full proofs. After introducing effective action, the chapter addresses loop expansion. The chapter ends with a discussion of Feynman diagrams in fermionic theory.

scholarly journals The construction of RFT from the Lipatov’s effective action

2018 ◽  
Vol 191 ◽  
pp. 04008
Author(s):  
Sergey Bondarenko ◽  
Semyon Pozdnyakov
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Equations Of Motion ◽  
Classical Solutions ◽  
Small X ◽  
Solutions Of Equations

We consider the formalism of small-x effective action for reggeized gluons, see [1-3]. We construct the perturbation theory based on the knowledge of the classical solutions of equations of motion (written with NNLO precision) and loops contributions to the effective action. Applications of the obtained results are also discussed.

scholarly journals Near conformal perturbation theory in SYK type models

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Sumit R. Das ◽  
Animik Ghosh ◽  
Antal Jevicki ◽  
Kenta Suzuki
Keyword(s):  
Perturbation Theory ◽  
Correlation Function ◽  
Effective Action ◽  
Correlation Functions ◽  
Conformal Invariance ◽  
Soft Mode ◽  
Energy Scale ◽  
Low Energy ◽  
Liouville Theory ◽  
Breaking Term

Abstract We present a systematic procedure to extract the dynamics of the low energy soft mode in SYK type models with a single energy scale J and emergent reparametrization symmetry in the IR. This is given in the framework of the perturbative scheme of arXiv:1608.07567 based on a specific (off-shell) breaking of conformal invariance in the UV, adjusted to yield the exact large-N saddle point. While this breaking term formally vanishes on-shell, it has a non-trivial effect on correlation functions and the effective action. In particular, it leads to the Schwarzian action with a specific coupling to bi-local matter. The method is applied to the evaluation of O(1) corrections to the correlation function of bi-locals. As a byproduct we confirm precise agreement with the explicit, symmetry breaking procedure. We provide a verification in the large q limit (Liouville theory), where the correlators can be calculated exactly at all length scales. In this case, our scheme illuminates how the enhanced O(J) and the subleading O(1) contributions originate from the Schwarzian dynamics of the soft mode and its interaction with h = 2 (bi-local) matter.

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