A functional approach to loop diagrams

1996 ◽  
Vol 74 (9-10) ◽  
pp. 614-617 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Heat Kernel ◽  
Background Field ◽  
Functional Approach ◽  
Closed Form Expression ◽  
Quantum Mechanical ◽  
Loop Order ◽  
Point Function ◽  
Form Expression ◽  
Generating Functional ◽  
Loop Contribution

A closed-form expression for the N-loop contribution to the generating functional can be written down using the heat kernel [Formula: see text]. If [Formula: see text] where Aμ and V are functions of the background field, then by using quantum-mechanical techniques, this heat kernel can be expanded in powers of the background field, allowing one to compute Green's functions. We demonstrate that one can also employ to this end a distinct functional approach developed by Onofri, which circumvents both loop-momentum integrals and the quantum-mechanical path integral. We illustrate the technique by computing the two-point function in scalar electrodynamics to one-loop order.

scholarly journals Exact four point function for large q SYK from Regge theory

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Changha Choi ◽  
Márk Mezei ◽  
Gábor Sárosi
Keyword(s):  
Lyapunov Exponent ◽  
Quantum Systems ◽  
Chaotic Regime ◽  
Closed Form Expression ◽  
Large Temperature ◽  
Complete Agreement ◽  
Leading Order ◽  
Point Function ◽  
Form Expression ◽  
Weakly Coupled

Abstract Motivated by the goal of understanding quantum systems away from maximal chaos, in this note we derive a simple closed form expression for the fermion four point function of the large q SYK model valid at arbitrary temperatures and to leading order in 1/N. The result captures both the large temperature, weakly coupled regime, and the low temperature, nearly conformal, maximally chaotic regime of the model. The derivation proceeds by the Sommerfeld-Watson resummation of an infinite series that recasts the four point function as a sum of three Regge poles. The location of these poles determines the Lyapunov exponent that interpolates between zero and the maximal value as the temperature is decreased. Our results are in complete agreement with the ones by Streicher [1] obtained using a different method.

The first-order formalism for Yang–Mills theory

1994 ◽  
Vol 72 (9-10) ◽  
pp. 601-607 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Background Field ◽  
Loop Order ◽  
Point Function ◽  
Yang Mills ◽  
First Order ◽  
Order Form ◽  
Effective Lagrangian ◽  
Gauge Fixing ◽  
Vector Formula ◽  
Field Quantization

It is possible to replace the second-order Yang–Mills Lagrangian [Formula: see text] with the first-order Lagrangian [Formula: see text]. In this form, the interaction term in the Lagrangian, [Formula: see text] is very simple; the only disadvantage is that now not only the vector [Formula: see text] but also the auxiliary field [Formula: see text] propagate. The gauge-fixing and ghost contributions to the effective Lagrangian can similarly be reduced to first-order form by the introduction of auxiliary fields. We demonstrate the procedure by computing the two-point function to one-loop order using background field quantization.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

Simple Closed-Form Expression to Estimate the Ring Ratio of 16-APSK to Compensate for Distortion in Nonlinear Systems

2017 ◽  
Author(s):  
M.J. Cañavate-Sánchez ◽  
A. Segneri ◽  
S. Godi ◽  
A. Georgiadis ◽  
S. Kosmopoulos ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Ring Ratio
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