Amplitudes in quantum field theory have discontinuities when regarded as

functions of

the scattering kinematics. Such discontinuities can be determined from

Cutkosky rules.

We present a structural analysis of such rules for massive quantum field

theory which combines

algebraic geometry with the combinatorics of Karen Vogtmann's Outer Space.

This is joint work with Spencer Bloch (arXiv:1512.01705).

# Past Quantum Field Theory Seminar

Hawking radiation and particle creation by an expanding Universe

are paradigmatic predictions of quantum field theory in curved spacetime.

Although the theory is a few decades old, it still awaits experimental

demonstration. At first sight, the effects predicted by the theory are too

small to be measured in the laboratory. Therefore, current experimental

efforts have been directed towards siumlating Hawking radiation and

studying quantum particle creation in analogue spacetimes.

In this talk, I will present a proposal to test directly effects of

quantum field theory in the Earth's spacetime using quantum technologies.

Under certain circumstances, real spacetime distortions (such as

gravitational waves) can produce observable effects in the state of

phonons of a Bose-Einstein condensate. The sensitivity of the phononic

field to the underlying spacetime can also be used to measure spacetime

parameters such as the Schwarzschild radius of the Earth.

[based on joint work with Li Guo and Bin Zhang]

We apply to the study of exponential sums on lattice points in

convex rational polyhedral cones, the generalised algebraic approach of

Connes and Kreimer to perturbative quantum field theory. For this purpose

we equip the space of cones with a connected coalgebra structure.

The algebraic Birkhoff factorisation of Connes and Kreimer adapted and

generalised to this context then gives rise to a convolution factorisation

of exponential sums on lattice points in cones. We show that this

factorisation coincides with the classical Euler-Maclaurin formula

generalised to convex rational polyhedral cones by Berline and Vergne by

means of an interpolating holomorphic function.

We define renormalised conical zeta values at non-positive integers as the

Taylor coefficients at zero of the interpolating holomorphic function. When

restricted to Chen cones, this yields yet another way to renormalise

multiple zeta values at non-positive integers.

In a quantum quench, a system is prepared in some state

$|\psi_0\rangle$, usually the ground state of a hamiltonian $H_0$, and then

evolved unitarily with a different hamiltonian $H$. I study this problem

when $H$ is a 1+1-dimensional conformal field theory on a large circle of

length $L$, and the initial state has short-range correlations and

entanglement. I argue that (a) for times $\ell/2<t<(L-\ell)/2$ the

reduced density matrix of a subinterval of length $\ell$ is exponentially

close to that of a thermal ensemble; (b) despite this, for a rational CFT

the return amplitude $\langle\psi_0|e^{-iHt}|\psi_0\rangle$ is $O(1)$ at

integer multiples of $2t/\ell$ and has interesting structure at all rational

values of this ratio. This last result is related to the modular properties

of Virasoro characters.