Presentation Slides

Question 1

01 : Title Slide

Answer 1

• Using tensor networks to represent scattering amplitudes
• Not a computing project, just the mathematical representation
• Aim is to contruct an accurate & flexible self-contained system

Question 2

02 : What is tensor notation

Answer 2

• Tensor notation = diagramatic tensor algebra (Boolean metaphor)
• Shapes represent tensors, legs represent indices
• Connected legs represent contracted indices

Question 3

03 : Penrose Graphical Notation

Answer 3

• Roger Penrose developed this for general relativity
• Here’s some examples (Bianchi identity)
• Emphisis on readablity to humans

Question 4

04 : Quantum Tensor Applications

Answer 4

• Tensor networks approximate quantum simulations (degrees of freedom)
• Ground-state Hamiltonian sweeping (red tensors are varied)
• PEPS Hilbert space for lattice gauge theory (virtual legs dimensions = entanglement between regions)

Question 5

05 : My approach to Feynman Diagrams

Answer 5

• It was decided to try & apply tensor notation to matrix elements (not Lagrangians)
• Aim is to improve the computability of scattering amplitude construction
• Feynman diagrams are good, but don’t scale well

Question 6

06 : Why Feynman diagrams don’t scale

Answer 6

• You need a huge number of diagrams
• The matrix elements become incredibly large
• My aim is to contruct amplitudes without needing to refer to mathematics

Question 7

07 : Particle Network Basics

Answer 7

• Explain the different means for each symbol
• Explain the original factorised space (which way lines contract)
• Show the modern layout with Feynman diagram

Question 8

08 : Electromagnetic Interactions

Answer 8

• Lines = quantum numbers. We only need spin & momentum lines.
• Differing vertex & propagator regions
• The effective field operator for Fermi interactions

Question 9

09 : Strong & Weak Interactions

Answer 9

• Strong & weak add new quantum number lines
• Strong : Gell-mann matrices
• Weak : PL/PR, mixing matrices & massive boson propagators

Question 10

10 : Necessary vs Aesthetic

Answer 10

• Middle of the road between Penrose & computers, more towards computers
• Constants have been absorbed into tensors
• Weak propagator was designed by necessity from the lines of contractions

Question 11

11 : Direct construction of process

Answer 11

• Main purpose = build networks without graphs
• Turn final states spinor into fermion propagator
• Add vertex terms, then new decay channel

Question 12

12 : Missing Vertices

Answer 12

• Missing Higgs & boson-boson coupling
• Need to do loop corrections & renormalisations
• Fully expect all of this to be done in next semester

Question 13

13 : Beyond the standard model

Answer 13

• Quantum gravity (problems with renormalisation)
• GUT theories: new field & bosons to explore
• Super-symmetry offers a huge number of new particles

Question 14

14 : Conclusion

Answer 14

• Aid computation of scattering amplitudes
• Aid comprhension of QFT processes
• Critical evaluation : have you succeeded in either?