Phd in Physics

Introduction to on-shell amplitudes

06-Introduction to on-shell amplitudes

Academic year 2023/2024

Sommario del corso

• Course objectives
• Results of learning outcomes
• Program
• Course delivery
• Learning assessment methods
• Suggested readings and bibliography
• Notes
• Teaching tools
• Course card

Course objectives

Introduce methods to uncover hidden simplicity in on-shell amplitudes for gauge theory and gravity.

* Spinor-helicity formalism

* Tree-level methods (colour ordering, off-shell and on-shell recursion)

* Loop-level methods (unitarity, generalised unitarity and integrand reduction)

* Loop integration methods (integration-by-parts reduction, differential equations)

Results of learning outcomes

Ability to solve simple problems with on-shell recursion and spinor helicity

Improved skills in computer algebra and analytic calculations

Overview of loop level structures and state-of-the-art results

Program

Scattering amplitudes can be seen as fundamental building blocks for Gauge, Gravity and String theories. The study of their mathematical structure has led to many new insights into connections between seemingly unrelated topics as well as enabling new computations unfeasible with conventional techniques. In this course I will cover some of the new methods that are now being used to provide efficient and precise predictions for higher order corrections at colliders. 1) Spinor-helicity methods for massless and massive particles. 2) Tree-level techniques: on-shell and off-shell recursion. 3) Loop amplitude techniques: unitarity, integrand reductions, IBPs and finite fields, differential equations and special functions. 4) New methods for gravity amplitudes: the double-copy and applications to gravitational waves.

Course delivery

Lectures accompianied with Mathematica exercises

Learning assessment methods

Homework exercises and final assessment, with the possibility for computer algebra solutions, will be submitted and feedback provided

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Notes

Students wishing to take this course must register with the teacher via email

Timetable:

Classes will be in Sala Fubini 15.00-17.00 unless stated otherwise

13/3, 14/3, 15/3,

20/3 (16:00-18:00), 21/3, 22/3,

10/4, 11/4, 12/4,

17/4, 18/4, 19/4

• Teaching material
• Exams and finals
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