Quantum Theory

Categorical Quantum Theory

a, b : C (states/systems/objects), f, g : a →_C b (processes/morphisms)

a = a_{i, j} e_i × e^j. f_a : H^* × H → C ⊢ f_a(v^*, v) = v^* a v, f_a(-, v) = a v = a_{i, j} v_j e_i. a = a_{i1, ⋯, in} e_i1 × ⋯ × e_in. a = a_{i1, ⋯, in, j1, ⋯, jn} e_i1 × ⋯ × e_in × e^j₁ × ⋯ × e^j_n.

Quantum algebra

Quantum Group

Quantum Field Theory

Quantum Phase Transition

References

• Topological Quantum Phases. Alexei Kitaev. 2019.
• Categories for Quantum Theory: An Introduction. Chris Heunen, Jamie Vicary. 2019.
• Modern Physics Formalized in Modal Homotopy Type Theory. Urs Schreiber. 2016.
• Quantum Gauge Field Theory in Cohesive Homotopy Type Theory. Urs Schreiber, Michael Shulman. 2014.