Related papers: Geometry and Localization, a metaphorically relate…
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…
We give an introduction for the non-expert to TQFT (Topological Quantum Field Theory), focussing especially on its role in algebraic topology. We compare the Atiyah axioms for TQFT with the Eilenberg Steenrod axioms for homology, give a few…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We extend the framework of general boundary quantum field theory (GBQFT) to achieve a fully local description of realistic quantum field theories. This requires the quantization of non-K\"ahler polarizations which occur generically on…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
Quantum operations that are perfectly admissible in non-relativistic quantum theory can enable signalling between spacelike separated regions when naively imported into quantum field theory (QFT). Prominent examples of such "impossible…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
Quantum Field Theory (QFT) represents a vast generalization of Quantum Mechanics (QM), as it deals with systems that have an infinite number of degrees of freedom. The Stone-von Neumann theorem, which establishes the equivalence of…
We introduce regular stratified piecewise linear manifolds to describe lattices and investigate the lattice model approach to topological quantum field theory in all dimensions. We introduce the unitary $n+1$ alterfold TQFT and construct it…
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(\phi)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this…
This is the first in a series of papers on an attempt to understand quantum field theory mathematically. In this paper we shall introduce and study BV QFT algebra and BV QFT as the proto-algebraic model of quantum field theory by exploiting…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of local effective field theory. Recently, we have…
In this paper we study the effect of localizing quantum field degrees of freedom by dynamically growing cavity walls through a time-dependent potential. We use our results to show that it is possible to do this without introducing…
We examine the notion of symmetry in quantum field theory from a fundamental representation theoretic point of view. This leads us to a generalization expressed in terms of quantum groups and braided categories. It also unifies the…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
Algebraic quantum field theory is an approach to relativistic quantum physics, notably the theory of elementary particles, which complements other modern developments in this field. It is particularly powerful for structural analysis but…
Within the algebraic setting of quantum field theory, a condition is given which implies that the intersection of algebras generated by field operators localized in wedge--shaped regions of two--dimensional Minkowski space is non--trivial;…
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation,…