Related Experiment Video
Updated: Jun 5, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Classical polylogarithms for amplitudes and Wilson loops
A B Goncharov1, M Spradlin, C Vergu
1Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912, USA.
Physical Review Letters
|January 15, 2011
Summary
Researchers derived a compact formula for the two-loop six-particle maximally helicity violating remainder function in N=4 supersymmetric Yang-Mills theory. This formula utilizes classical polylogarithm functions and momentum twistor invariants, simplifying complex calculations in theoretical physics.
Area of Science:
- Theoretical High Energy Physics
- Quantum Field Theory
- Supersymmetry
Background:
- The study of scattering amplitudes in N=4 supersymmetric Yang-Mills theory is crucial for understanding quantum field theories.
- Calculating multi-loop amplitudes, such as the six-particle case, presents significant theoretical challenges.
Purpose of the Study:
- To derive a compact analytic formula for the two-loop six-particle maximally helicity violating (MHV) remainder function.
- To express this function in terms of established mathematical objects like classical polylogarithms.
Main Methods:
- The derivation employs results from the theory of motives.
- The formula relates the remainder function to cross ratios of momentum twistor invariants.
Main Results:
- A compact analytic formula for the two-loop six-particle MHV remainder function has been established.
- The formula is expressed using classical polylogarithm functions (Li_k) with momentum twistor invariants as arguments.
Conclusions:
- The presented formula offers a significant simplification for calculating specific amplitudes in N=4 supersymmetric Yang-Mills theory.
- This work connects concepts from scattering amplitudes, polylogarithms, and the theory of motives, advancing theoretical physics research.
Related Concept Videos
01:24Pole and System Stability
The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
01:28Laws of Logarithms II
Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
01:30Laws of Logarithms I
Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...
01:14Introduction to Logarithmic Functions
Logarithmic functions are the inverses of exponential functions and are used to solve for exponents. The general form is y = logₐ(x), where a > 0 and a ≠ 1. This function returns the power to which the base a must be raised to obtain x. The logarithmic function is only defined for x > 0, and its range includes all real numbers.Graphically, logarithmic and exponential functions are reflections of each other across the line y = x. The graph of y = logₐ(x) passes through (1, 0) and has a...
01:28Types of Functions III
Logarithmic and piecewise functions play central roles in mathematical modeling, particularly when capturing nonlinear or segmented behaviors in real-world phenomena. Although these functions differ fundamentally in structure and application, both serve to represent complex relationships in simplified mathematical terms.A logarithmic function is defined as the inverse of an exponential function, expressed as These functions grow quickly for small values of x but slow down as x increases,...
01:23Transfer function and Bode Plots-II
In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero: