AG Mathematische Physik, Daniela Cadamuro (Leipzig): The massive modular Hamiltonian in the case of bosons and fermions und Jakob Hedicke (Montreal): On spaces of light rays and contact structures

Daniela Cadamuro (Leipzig)

The massive modular Hamiltonian in the case of bosons and fermions

Abstract:

The Tomita-Takesaki modular operator for local algebras plays an

important role in quantum field theory, and more recently in the study

of relative entropy. However, the explicit expression of this

operator, except for the case of wedges, is difficult to describe

mathematically. We have obtained numerical results for the form of the

modular Hamiltonian for a double cone in a massive scalar free field

in (1+1)- and (3+1)-dimensional Minkowski space, which shows how it

differs from the wedge case, in particular regarding the dependence of

the modular Hamiltonian on the mass of the field. We also obtained

results for the free massive Majorana fermions in 1+1 dimensions in

the cases of a single and two double cones, and point out the

differences with the bosonic case.

Jakob Hedicke (Toronto)

On spaces of light rays and contact structures

Abstract:

As first observed in the works of Penrose and Low, in many cases the

space of light rays of a Lorentzian spacetime can be naturally equipped

with the structure of a smooth contact manifold.

In these cases the contact geometry of the space of light rays has

strong connections to the causality of the underlying Lorentzian manifold.

After an introduction to the relevant notions from contact- and

Lorentzian geometry, we will discuss criteria that ensure the space of

light rays to be a contact manifold and we will determine its contact

structure in several examples.