Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1711.08829

A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory

V. A. Guskov·M. G. Ivanov·S. L. Ogarkov
View original source ↗Read source document ↗Export metadata ↓

Abstract

In frames of the nonlocal and nonpolynomial quantum theory of the one component scalar field in $D$-dimensional spacetime, stated by Gariy Vladimirovich Efimov, the expansion of the $\mathcal{S}$-matrix is revisited for different interaction Lagrangians and for some kinds of Gaussian propagators modified by different ultraviolet form factors $F$ which depend on some length parameter $l$. The expansion of the $\mathcal{S}$-matrix is of the form of a grand canonical partition function of some $D+N$-dimensional ($N\geq 1$) classical gas with interaction. The toy model of the realistic quantum field theory (QFT) is considered where the $\mathcal{S}$-matrix is calculated in closed form. Then, the functional Schwinger-Dyson and Schrödinger equations for the $\mathcal{S}$-matrix in Efimov representation are derived. These equations play a central role in the present paper. The functional Schwinger-Dyson and Schrödinger equations in Efimov representation do not involve explicit functional derivatives but involve a shift of the field which is the $\mathcal{S}$-matrix argument. The asymptotic solutions of the Schwinger-Dyson equation are obtained in different limits. Also, the solution is found in one heuristic case allowing us to study qualitatively the behavior of the $\mathcal{S}$-matrix for an arbitrary finite value of its argument. Self-consistency equations, which arise during the process of derivation, are of a great interest. Finally, in the light of the discussion of QFT functional equations, ultraviolet form factors and extra dimensions, the connection with functional (in terms of the Wilson-Polchinski and Wetterich-Morris functional equations) and holographic renormalization groups (in terms of the functional Hamilton-Jacobi equation) is made. In addition the Hamilton-Jacobi equation is formulated in an unconventional way.

Explore related subjects

hep-thcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

V. A. Guskov, M. G. Ivanov, S. L. Ogarkov. 2020-12-24. A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory. https://doi.org/10.1134/s1063779621030059

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fortuitous Chaos, BPS Black Holes, and Random Matrices

The ``fortuitous'' Bogomol'nyi-Prasad-Sommerfield (BPS) sector states in gauge theory have been argued to furnish a description, through holography, of generic BPS black hole microstates. They are expected to be strongly chaotic, a necessary feature to capture the black hole dynamics. This dovetails nicely with the existence of various random matrix models of JT supergravity with extended supersymmetry, within which the BPS chaos must be contained as a subsector. This paper identifies and studies a simple random matrix model that underlies all known random matrix models of JT supergravity. It is argued that it captures many essential universal features of fortuitous BPS chaos. The model is topological, naturally interpolating between the Bessel and Airy models, where the gap energy $E_0$ controls the interpolation, and seems to have a simple intersection theory interpretation.

hep-th↗
arXiv2026

Introduction to Generalized Symmetries

These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in $(1+1)$-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to $(3+1)$-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.

hep-th↗
arXiv2026

Planar loop integrands from cuts in $D$ dimensions

We present a direct reconstruction formula for planar loop integrands from $D$-dimensional generalized unitarity cuts in any colored theory. The reconstruction combinatorics is separated from the theory-dependent tree amplitudes entering the cuts: for the $L$-loop $n$-point color-ordered amplitude, the integrand is expressed as a sum over admissible non-scaleless scalar graphs dressed by corresponding cuts in $D$ dimensions; the coefficients are given by the universal Möbius-inversion formula of the refinement poset, or equivalently one minus the Euler characteristics of associated complexes. As an application we write down closed-formulas for loop integrands in pure Yang--Mills theory, where the required cuts are generated by gluing $D$-dimensional tree amplitudes and summing over internal gluon states. We also use the two-loop five-point case as a validation, comparing with known integrand data and after integration-by-parts reduction, with known integrated helicity amplitudes. The same framework also produces compact cut-organized data for larger examples, including the two-loop six-point and three-loop four-point cases. We also describe the corresponding simplification in maximally supersymmetric Yang--Mills theory, where the absence of bubble and triangle subgraphs reduces the relevant cut poset substantially.

hep-th↗