https://github.com/christianparsons98/positronium-qed-projects

Projects relating to Fortran, Reduce, and Mathematica QED calculations of Positronium.

https://github.com/christianparsons98/positronium-qed-projects

Repository

Projects relating to Fortran, Reduce, and Mathematica QED calculations of Positronium.

https://github.com/ChristianParsons98/Positronium-QED-Projects/blob/main/

# Positronium-QED-Projects

This repository contains computational tools and scripts developed for high-precision calculations in positronium quantum electrodynamics (QED). The work has contributed to three peer-reviewed publications:

- **Three-Photon-Annihilation Contributions to Positronium Energies at Order m**  
  *Phys. Rev. Lett. 115, 233401 (2015)*  
  [Link to paper](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.233401)

- **Positronium Energy Levels at Order m: Light-by-Light Scattering in the Two-Photon-Annihilation Channel**  
  *Phys. Rev. A 90, 042502 (2014)*  
  [Link to paper](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.90.042502)

- **Vacuum Polarization Corrections in the Two-Photon-Annihilation Channel**  
  *Phys. Lett. B 746, 551555 (2015)*  
  [Link to paper](https://www.sciencedirect.com/science/article/pii/S0370269315004724)

##  Description

The code in this repository performs high-order QED calculations for positronium, focusing on:

- Three-photon annihilation contributions to energy levels.
- Light-by-light scattering effects in two-photon annihilation channels.
- Vacuum polarization corrections in annihilation processes.

These calculations are essential for refining theoretical predictions of positronium energy levels and decay rates, providing stringent tests of bound-state QED.

##  Techniques Used

- **Feynman Diagram Computation**: Automated evaluation of complex Feynman diagrams.
- **Dimensional Regularization**: Handling divergences in loop integrals.
- **Numerical Integration**: High-precision computation of multi-dimensional integrals.
- **Symbolic Algebra**: Simplification and manipulation of mathematical expressions.

##  Libraries and Tools

- [FORM](https://www.nikhef.nl/~form/): Symbolic manipulation system for high-energy physics.
- [Mathematica](https://www.wolfram.com/mathematica/): Computational software for symbolic and numerical calculations.
- [Python](https://www.python.org/): General-purpose programming language for scripting and automation.

##  Project Structure

```plaintext
.
 diagrams/
 integrals/
 scripts/
 results/
 README.md
```

### Notable Directories

- `diagrams/`: Definitions and representations of Feynman diagrams.
- `integrals/`: Scripts and data for evaluating loop integrals.
- `scripts/`: Automation scripts for running calculations.
- `results/`: Output data and results from computations.

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