The inevitability of physical laws
Can we recover known physics from basic principles alone?
Quantum field theory is far less arbitrary than it appears. Self-consistency strongly constrains what is possible, and some familiar laws may follow inevitably. This is seen most clearly in scattering amplitudes, where complicated calculations often collapse into remarkably simple answers involving positive geometries, cluster algebras, combinatorics, and special functions. These surprising structures suggest that a deeper formalism—beyond standard QFT and traditional Lagrangian methods—remains to be discovered.
If consistency is so powerful, what can it teach us about quantum gravity? Can we obtain rigorous, model-independent results without assuming string theory or relying on black-hole physics?
These questions lead to the *space of all allowed theories*. We will explore it through uniqueness theorems and the analytic S-matrix bootstrap, asking: Which theories are possible? And where does string theory sit in the space of all allowed theories?
The course will progress from foundational calculations to modern methods and current research. Homework will begin with guided calculations and gradually develop into open-ended problems. The course may include a short research project based on an accessible open question.
Quantum field theory is far less arbitrary than it appears. Self-consistency strongly constrains what is possible, and some familiar laws may follow inevitably. This is seen most clearly in scattering amplitudes, where complicated calculations often collapse into remarkably simple answers involving positive geometries, cluster algebras, combinatorics, and special functions. These surprising structures suggest that a deeper formalism—beyond standard QFT and traditional Lagrangian methods—remains to be discovered.
If consistency is so powerful, what can it teach us about quantum gravity? Can we obtain rigorous, model-independent results without assuming string theory or relying on black-hole physics?
These questions lead to the *space of all allowed theories*. We will explore it through uniqueness theorems and the analytic S-matrix bootstrap, asking: Which theories are possible? And where does string theory sit in the space of all allowed theories?
The course will progress from foundational calculations to modern methods and current research. Homework will begin with guided calculations and gradually develop into open-ended problems. The course may include a short research project based on an accessible open question.
Lecturer
Date
6th October ~ 22nd December, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday | 15:20 - 18:40 | Qiuzhen | ZOOM 13 | 637 734 0280 | BIMSA |
Prerequisite
Basic notions of QFT
Syllabus
1. Feynman diagrams and scattering amplitudes
Basic calculations and the physical meaning of amplitudes.
2. Consistency in quantum field theory
Symmetry, locality, unitarity, causality.
3. Beyond Feynman diagrams
On-shell methods, amplitudes via curve counting.
4. Uniqueness of physical laws
Deriving gauge theory and gravity from consistency.
5. Gravity as Yang–Mills squared
Color–kinematics duality and the double copy.
6. The analytic S-matrix
Analyticity, crossing symmetry, dispersion relations, and positivity.
7. The space of allowed theories
Uniqueness theorems and the S-matrix bootstrap.
8. String theory from consistency
String amplitudes and their place in the space of theories.
9. New mathematics from scattering
Positive geometries, cluster algebras, combinatorics, and special functions.
10. Quantum gravity
Model-independent constraints and swampland conjectures
Basic calculations and the physical meaning of amplitudes.
2. Consistency in quantum field theory
Symmetry, locality, unitarity, causality.
3. Beyond Feynman diagrams
On-shell methods, amplitudes via curve counting.
4. Uniqueness of physical laws
Deriving gauge theory and gravity from consistency.
5. Gravity as Yang–Mills squared
Color–kinematics duality and the double copy.
6. The analytic S-matrix
Analyticity, crossing symmetry, dispersion relations, and positivity.
7. The space of allowed theories
Uniqueness theorems and the S-matrix bootstrap.
8. String theory from consistency
String amplitudes and their place in the space of theories.
9. New mathematics from scattering
Positive geometries, cluster algebras, combinatorics, and special functions.
10. Quantum gravity
Model-independent constraints and swampland conjectures
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Laurentiu Rodina obtained his PhD from Princeton University, under the supervision of Nima Arkani-Hamed. He was a postdoctoral fellow at CEA Saclay-Paris and National Taiwan University, and a Marie Curie Fellow at Queen Mary University of London. He joined BIMSA as assistant professor in 2023 and since 2025 is associate professor. His research is focused on bootstrap approaches in QFT and CFT: describing the space of theories consistent with fundamental physical principles.