In this doctoral thesis, we develop and investigate new mathematical tools that are intended to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics. Here, the term QFT is to be understood ...

In quantum field theory (QFT) models, it often seems natural to use, instead of wave functions from Fock space, wave functions that are not square-integrable and have prefactors involving divergent integrals (known as ...

During the last three decades, P. Bóna has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence ...

We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on ...

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b -symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864–896, we ...

We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known ...

The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity ...

In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well ...

The Kubo-Martin-Schwinger (KMS) condition is a widely studied fundamental property in quantum statistical mechanics which characterizes the thermal equilibrium states of quantum systems. In the seventies, Gallavotti and ...

We study the macroscopic dynamical properties of fermion and quantum-spin systems with long-range, or mean-field, interactions. The results obtained are far beyond previous ones and require the development of a mathematical ...