Questions tagged [hopf-algebra]

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When do the solutions of combinatorial Dyson-Schwinger equations generate a Hopf subalgebra?

Say I have a set of combinatorial Dyson-Schwinger equations of the form $$\begin{align} X_1 &= \mathbb{1} + \alpha B_+^a (f_1(X_1,...X_N)) \\ & ... \tag{1} \\ X_N &= \mathbb{1} + \alpha ...
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External structure in BPHZ/Hopf algebraic renormalization of QED

I'm currently trying to understand and reproduce the Hopf-algebraic renormalization of QED presented by Walter D. Van Suijlekom. I don't understand why he chooses these external structures in (2), (7),...
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Hopf Algebras in Quantum Groups

In the theory of quantum groups Hopf algebras arise via the Fourier transform: A third point of view is that Hopf algebras are the next simplest category after Abelian groups admitting Fourier ...
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Boson calculus and Maximum Weight State

I'm just going over a few past exams for tomorrow, and I've come across a question that I'm having quite a bit of difficulty with. Let $\left|0\right\rangle$ denote the Fock vacuum state so that $...
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What are the uses of Hopf algebras in physics?

Hopf algebra is nice object full of structure (a bialgebra with an antipode). To get some idea what it looks like, group itself is a Hopf algebra, considered over a field with one element ;) usual ...
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Why do string theory and Hopf algebra renormalization seem to have no intersection?

Hopf algebra appears in recent papers that systematize renormalization of quantum field theory (QFT). For example see Connes' work and citing papers or a paper referenced here on PSE: R. E. Borcherds,...