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Now showing items 1-10 of 41

#### Time Dynamics in Quantum Field Theory Systems

(2022-12-23)

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 ...

#### Extended State Space for Describing Renormalized Fock Spaces in QFT

(2022-06-04)

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 ...

#### Classical dynamics from self-consistency equations in quantum mechanics

(2022-05-09)

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 ...

#### Implementing Bogoliubov Transformations Beyond the Shale-Stinespring Condition

(2022-04-28)

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 ...

#### Weak* Hypertopologies with Application to Genericity of Convex Sets

(2022)

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 ...

#### Entanglement of classical and quantum short-range dynamics in mean-field systems

(2021-11-01)

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 ...

#### Another Proof of Born's Rule on Arbitrary Cauchy Surfaces

(2021-10-14)

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 ...

#### High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graph

(2021-08-01)

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 ...

#### Classical dynamics generated by long-range interactions for lattice fermions and quantum spins

(2021)

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 ...

#### Large Deviations in Weakly Interacting Fermions - Generating Functions as Gaussian Berezin Integrals and Bounds on Large Pfaffians

(2021)

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ...