Abstract
Homological technics have been widely used in physics for a very long time.
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Notes
- 1.
We refer to [27] and references therein for an introduction to derived geometry.
- 2.
We won’t detail what non-degeneracy means here, but simply say that its definition again mimics the main abstract feature of relative Poincaré duality.
- 3.
Here an below, \(\overline{??}\) means that we consider the opposite integration theory or the opposite symplectic structure on \(??\) (it should be clear from the context).
- 4.
This is a joint project with Giovanni Felder.
- 5.
Roughly, \(\mathcal F_R\) carries a discrete flat connection and \(\widetilde{\mathcal F}_R\) is the factorization algebra of derived flat sections of \(\mathcal F_R\).
- 6.
This is very much related to the fact that the symplectic structure on \(BG\) is zero. In the case of compact groups, \(Rep(G)\) isn’t finite enough and must be deformed in order to get a rigid enough object... this is where the quantum group comes from.
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Calaque, D. (2015). A Derived and Homotopical View on Field Theories. In: Calaque, D., Strobl, T. (eds) Mathematical Aspects of Quantum Field Theories. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-09949-1_1
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