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Predicting the behavior of systems consisting of many mutually interacting parts is known as the many-body problem. It presents itself for example in astronomy, where the precise orbit of any celestial body depends on the orbits of all nearby bodies. The problem is also encountered on the level of quantum particles. For example the electronic and optical properties of materials often follow from complex interactions of electrons among themselves.

In many-body quantum theory the possible interaction processes between individual particles are separated and expressed in terms of diagrams. Any collection of such diagrams can be used to build an approximate model in which particles interact only in specific ways. This allows for great freedom in choosing for any situation an approximation that includes the necessary physics without being needlessly complicated.

This freedom comes with certain pitfalls, in that it also allows models that violate fundamental properties of the real system. The appearance of negative probabilities is one such violation. This not only makes the interpretation of the results impossible but can also lead to issues in numerical algorithms.

The issue of negative probabilities has been previously solved for systems in zero temperature. However, generalization to finite temperature involves additional challenges. These arise since treating the finite temperature using statistical physics involves probabilities reflecting uncertainty about the precise state of the system. Combining these classical probabilities with the fundamental probabilistic nature of quantum mechanics makes the precise physical content of the resulting diagrams more difficult to determine.

In this dissertation so called finite temperature cutting rules are derived. These rules are used to cut diagrams into more fundamental pieces describing collisions between particles. These pieces can be combined again into full diagrams in a way that preserves necessary symmetry properties to guarantee non-negative probabilities. This also results in an approximation with clear physical content in terms of particle collisions that it allows.

The public examination of dissertation of Markku Hyrkäs, “Cutting Rules in Non-Equilibrium Many-Body Theory” will be held 29.9.2022 at 12 noon in the department of chemistry hall KEM1. The opponent is Associate Professor Gianluca Stefenucci (University of Rome Tor Vergata) and custos is Professor Robert van Leeuwen (Ģ��ֱ��). The language of the dissertation is English.

The dissertation is .

The dissertation research was financially supported by Väisälä Foundation and the Finnish Cultural Foundation.