# North British Mathematical Physics Seminar 53

The fifty third meeting of the North British Mathematical Physics Seminar took place on

Friday 11th May 2018 at the King's Manor, University of York.

The King's Manor is in the centre of the city, 5 minutes' walk from the railway station. To get there, turn left out of the station, under the wall, left over the bridge over the river, then left after 100m at the crossroads (see map). The King's Manor is in Exhibition Square, to the left of the fountain and the city art gallery.

Refreshments will be in the refectory and lunch in cafes nearby. To get to the refectory go through the porters' lodge and up the stone staircase towards the end of the first court on the left. Talks will be in K/133, entered either through the refectory (back of the theatre) or at the far left-hand corner of the furthest court (which brings you in at the front of the theatre).

## Programme

1030-1100
Coffee
1100-1200
Eleni Kontou (York)
Hawking's singularity theorem concerns matter obeying the strong energy condition (SEC), which means that all observers experience a nonnegative effective energy density (EED), thereby guaranteeing the timelike convergence property. However, for both classical and quantum fields, violations of the SEC can be observed in some of the simplest of cases, like the massive Klein-Gordon field. Therefore there is a need to develop theorems with weaker restrictions, namely energy conditions averaged over an entire geodesic and quantum inequalities, weighted local averages of energy densities. We have derived lower bounds of the EED in the presence of both classical and quantum scalar fields allowing nonzero mass and nonminimal coupling to the scalar curvature. In the quantum case these bounds take the form of a set of state-dependent quantum energy inequalities valid for the class of Hadamard states. Finally, we discuss how these lower bounds are applied to prove Hawking-type singularity theorems asserting that, along with sufficient initial contraction at a compact Cauchy surface, the spacetime is future timelike geodesically incomplete.
1200-1345
Lunch
1345-1445
Nabil Iqbal (Durham)
1445-1530
Tea
1530-1600
Lukas Müller (Heriot-Watt)

In this talk I will discuss a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally non-geometric flux backgrounds, which naturally allows for representations of nonassociative magnetic translation operators.

Concretely, I will explain how one can use the 2-Hilbert space of sections of a bundle gerbe in a putative framework for canonical quantisation and define a parallel transport on bundle gerbes on R^d which naturally furnishes weak projective 2-representations of the translation group on this 2-Hilbert space. The talk is based on joint work with Severin Bunk and Richard J. Szabo.

1600-1700
Markus Fröb (York)
We show that every (graded) derivation on the algebra of free quantum fields and their Wick powers in curved spacetimes gives rise to a set of anomalous Ward identities for time-ordered products, with an explicit formula for their classical limit. We study these identities for the Koszul-Tate and the full BRST differential in the BV-BRST formulation of perturbatively interacting quantum gauge theories, and show that the quantum BRST differential, the quantum antibracket and the higher-order anomalies form an $L_\infty$ algebra. The defining relations of this algebra ensure that the gauge structure is well-defined on cohomology classes of the quantum BRST operator, i.e., on the interacting observables. Furthermore, we show that one can determine contact terms such that also the interacting time-ordered products of multiple interacting fields are well defined on cohomology classes. The talk is based on arXiv:1803.10235.

## Practical Information

These maps will get you from the railway station to King's Manor (the university-provided one doesn't show the station).

If you come by car I'm afraid you'll need to take your chances in the city centre car parks. Bootham Row is the closest council car park, but the much larger Marygate is the next closest.

Limited funds are available to help with travel expenses of those with no other source of funding, especially postgraduate students and postdocs. Please book early to take advantage of the cheaper advance-purchase train fares. For how to claim please see the main NBMPS page.

If you have any questions, please email the local organiser, Eli Hawkins. There is no need to notify us in order to attend.