Katarzyna Rejzner: Quantum master equations with boundaries: pAQFT meets BV-BFV
| Dates: | 16 November 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Speaker: | Katarzyna Rejzner (York) |
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Abstract:
The BV formalism encodes the gauge structure of a field theory in odd symplectic geometry. Its central object is the quantum master equation, which fails once spacetime has a boundary. In the BV-BFV programme of Cattaneo, Mnev and Reshetikhin (CMR), this failure is compensated by a BFV structure on the boundary, which gives a modified classical and quantum master equation. Rigorous results in this programme have so far mostly come from topological examples such as BF and Chern–Simons theory. In this talk I will present joint work with Michele Schiavina in which we bring these ideas into perturbative algebraic quantum field theory (pAQFT). We work with gauge theories on globally hyperbolic Lorentzian manifolds with marked hypersurfaces, which we treat as “smoothened” boundaries. We formulate the modified master equations in this setting and construct a renormalised quantum BFV operator whose boundary terms correct the failure of the quantum master equation. On the algebraic side, the homotopy Lie algebra that comes from the anomalous Master Ward Identity becomes curved: the boundary contributions show up as a curvature term of an L_?-algebra. As applications, I will show how this recovers Hollands’ relation between the boundary BRST charge and the BV operator. In Abelian Yang–Mills theory on causal cylinders, it also reproduces the Cattaneo–Mnev–Reshetikhin quantum BFV ansatz at leading order.
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Frank Adams room 1
Alan Turing Building
Manchester
