Related papers: Morse Theory in Field Theory
It is shown how to obtain state vectors associated with measurements on the separated subystems of an entangled state, revealing how a single wavefunction encodes a set of statistical measurement outcomes. The result explains why…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
The goal of this work is to describe a categorical formalism for (Extended) Topological Quantum Field Theories (TQFTs) and present them as functors from a suitable category of cobordisms with corners to a linear category, generalizing 2d…
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
We propose a theory for coupling matter fields with discrete geometry on higher-order networks, i.e. cell complexes. The key idea of the approach is to associate to a higher-order network the quantum entropy of its metric. Specifically we…
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance behavior of condensed matter systems. Often…
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…
The Bell-Clauser-Horne-Shimony-Holt inequality can be used to show that no local hidden-variable theory can reproduce the correlations predicted by quantum mechanics (QM). It can be proved that certain QM correlations lead to a violation of…
First steps are taken in a project to construct a general class of conformal and perhaps, eventually, non-conformal quantum field theories of (n-1)-dimensional extended objects in a d=2n dimensional conformal space-time manifold M. The…
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce some basic notions of Topological Quantum…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a…
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
In many cases the symmetry structure of quantum field theories can be neatly encoded into their associated symmetry topological field theory (SymTFT), a topological field theory in one dimension higher. For geometrically engineered QFTs in…
The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…
We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…