// Research & Academic Vault

Documents

Mathematica notebooks, problem sets, and academic documents spanning integrable models, general relativity, and theoretical physics coursework.

5 Integrability
1 General Relativity
1 Lie Groups and Lie Algebras
6 Academic

Integrability Documents

5 files
Mathematica NotebookFeatured

Defect Sum

Give a twist function and the code will calculate the zeros, poles, levels, and the defect sum.

Mathematica NotebookFeatured

SU(2) η-Deformed ℤ₂-Twisted η-Model

For given SU(2) generators, a general field element of SU(2), R-matrix that satisfies the modified classical Yang-Baxter equation, and ℤ₂ automorphism, the code computes the currents j=g⁻¹∂g, the Lax matrix, the Lagrangian, equations of motion, flatness of the Lax, and the metric and B-field.

Mathematica Notebook

SU(2) λ-Deformed ℤ₂-Twisted η-Model

For given SU(2) generators, a general field element of SU(2), R-matrix that satisfies the modified classical Yang-Baxter equation, and ℤ₂ automorphism, the code computes the currents j=g⁻¹∂g, the Lax matrix, the Lagrangian, equations of motion, flatness of the Lax, and the metric and B-field.

Mathematica Notebook

SU(2) η-Deformed ℤ₂-Twisted λ-Model

For given SU(2) generators, a general field element of SU(2), R-matrix that satisfies the modified classical Yang-Baxter equation, and ℤ₂ automorphism, the code computes the currents j=g⁻¹∂g, the Lax matrix, the Lagrangian, equations of motion, flatness of the Lax, and the metric and B-field.

Mathematica Notebook

SU(2) λ-Deformed ℤ₂-Twisted λ-Model

For given SU(2) generators, a general field element of SU(2), R-matrix that satisfies the modified classical Yang-Baxter equation, and ℤ₂ automorphism, the code computes the currents j=g⁻¹∂g, the Lax matrix, the Lagrangian, equations of motion, flatness of the Lax, and the metric and B-field.

General Relativity Documents

1 file
Mathematica NotebookFeatured

Metric

Give the dimension of the manifold, the coordinates, and the metric — the code calculates the inverse metric, Christoffel symbols, Riemann curvature tensor, Ricci tensor, scalar curvature, and Einstein tensor.

Lie Groups and Lie Algebras Documents

1 file
Mathematica NotebookFeatured

SU(N) Generators

Generators of the SU(N) Lie algebra in the fundamental representation, including the structure constants and the d-coefficients.

Academic Documents

6 files
PDF

Final Exam: Computational Physics

Final exam paper for the Computational Physics module.

PDF

Homework: Quantum Electrodynamics

Homework assignment for the Quantum Electrodynamics module.

PDF

Homework: General Relativity

Homework assignment for the General Relativity module.

PDF

Homework: Group Theory

Homework assignment for the Group Theory module.

PDF

Homework: Quantum Field Theory

Homework assignments for the Quantum Field Theory module, split into two parts.

PDF

Homework: Standard Model

Homework assignment for the Standard Model module.