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Now showing items 1-10 of 10

#### 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 ...

#### Linearization of holomorphic families of algebraic automor- phisms of the affine plane

(2022-01-03)

Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular ...

#### 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 ...

#### Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature

(2022)

ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...

#### Uniform Lech's inequality

(2022)

Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(Rred) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...

#### COHOMOLOGY OF CONTACT LOCI

(2022-01-01)

We construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with ...

#### A b-symplectic slice theorem

(2022-01-01)

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 ...