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Quadratic Hamiltonians in Fermionic Fock Spaces

Bru, J.-B.; Métraud, N.J.H. (2025-01-01)

Quadratic Hamiltonians are important in quantum field theory and quantum statistical mechanics. Their general studies, which go back to the sixties, are relatively incomplete for the fermionic case studied here. Following Be...

Scattering and Pairing by Exchange Interactions

Bru, J.-B.; de Siqueira Pedra, W.; Ramer dos Santos, A. (2025-01-01)

Quantum interactions exchanging different types of particles play a pivotal rôle in quantum many-body theory, but they are not sufficiently investigated from a mathematical perspective. Here, we consider a system made of two...

Non-Linear Operator-valued Elliptic Flows with Application to Quantum Field Theory

Bru, J.-B.; Métraud, N.J.H. (2025-01-01)

Differential equations on spaces of operators are very little developed in Mathematics, being in general very challenging. Here, we study a novel system of such (non-linear) differential equations. We show it has a unique so...

C*-Algebraic Formulation of Quantum Mechanics

Bru, J.-B.; de Siqueira Pedra, W. (2025-01-01)

This manuscript is based on a series of lectures given in the XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering. While quantum mechanics is widely presented within the Hilbert spa...