https://github.com/cianlm/symbolicquantumfieldtheory.jl

Symbolic QFT in Julia
https://github.com/cianlm/symbolicquantumfieldtheory.jl

julia particle-physics physics qft quantum science symbolic

Last synced: about 1 month ago
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Symbolic QFT in Julia

• Host: GitHub
• URL: https://github.com/cianlm/symbolicquantumfieldtheory.jl
• Owner: CianLM
• License: gpl-2.0
• Created: 2022-11-19T13:43:11.000Z (about 2 years ago)
• Default Branch: main
• Last Pushed: 2024-09-18T02:33:15.000Z (4 months ago)
• Last Synced: 2024-09-18T06:05:30.957Z (4 months ago)
• Topics: julia, particle-physics, physics, qft, quantum, science, symbolic
• Language: Julia
• Homepage:
• Size: 121 KB
• Stars: 8
• Watchers: 2
• Forks: 0
• Open Issues: 5
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# SymbolicQuantumFieldTheory.jl

[![Build Status](https://github.com/CianLM/QFT.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/CianLM/QFT.jl/actions/workflows/CI.yml?query=branch%3Amain)

## Symbolic Quantum Field Theory in Julia

This package is in active development and is not production ready. Feel free to reach out with suggestions/issues.

Documentation is under construction. See `test.ipynb` for LaTeX printing and more example usage.

## Basic Syntax

```julia

using QFT

using Symbolics

@operator ScalarField a

@syms p q

```

where `a` is the name of the operator and `p` and `q` are the momenta.

We can use these objects with

```julia

comm(a(p),a(q)')

normalorder(a(p) * a(q)')

a(p)'^2 * a(q)' * vacuum()

ℋ = E(q) * a(q)' * a(q)

integrate(ℋ * a(p)', q)

```

which returns $2\pi * E(p) a_p^\dagger \ket{0}$ in a Jupyter notebook and `2π*E(p)a_p^†|0⟩` otherwise.

## Defining a Custom Commutation Relation

We can define a custom commutation relation between operators in a field using a natural syntax with the `@comm` macro.

*Note*. To do this we need to

```julia

import QFT.comm

```

as the `comm` function will be overloaded with your custom relation.

Then,

```julia

@field YourField

@operators YourField b c

@comm [b(p), c(q)'] = f(p,q)

```

for any `f(p,q)`.

This defines the commutation relation such that the commutator is now given by

```julia

@syms k l 

comm(b(k), c(l)') # returns f(k,l)

```

where Julia has replaced `p` and `q` with `k` and `l` appropriately. Multiple indices are also supported with `@comm [b(p,q), c(r,s)'] = f(p,q,r,s)`.