TQFT (The Topological Quantum Field Theory Song)

Поділитися
Вставка
  • Опубліковано 4 жов 2024
  • Lyrics:
    I've got a one dimensional QFT
    It's pretty straightforward topologically
    In this case it's just a vector space
    But if you want to talk categorically
    A morphism is an oriented line
    Between points with a plus or minus sign
    It's equivalent to "dual pairs"
    And that's a category that I won't define
    I just need a functor for my quantum field theory
    Will it be monoidal? You bet it better be
    I'll take it symmetric, but don't give me a metric
    It's only topological to me
    Dimension two is a little more fun
    Objects are generated by S^1
    Classify the surface with Morse theory
    And there you've got a bordism category
    Designate a vector space
    As a functor that's your fate
    As a groupoid it's the equivalent of
    Commutative Frobenius algebras
    I just need a functor for my quantum field theory
    Will it be monoidal? You bet it better be
    I'll take it symmetric, but don't give me a metric
    It's only topological to me
    Now it's time for dimension three
    Knock knock whose there higher category theory
    Infinite generators just won't do
    So we'll take morphisms to level two
    I've read all the papers
    A categoric adventure
    I still don't know what it means
    To be "modular tensor"
    I just need a functor for my quantum field theory
    Will it be monoidal? You bet it better be
    I'll take it symmetric, but don't give me a metric
    It's only topological to me
    I just need a functor for my quantum field theory
    Will it be monoidal? You bet it better be
    I'll take it symmetric, but don't give me a metric
    It's only topological to me

КОМЕНТАРІ • 51