Related papers: A geometric perspective on Algebraic Quantum Field…
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT,…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum…
The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that…
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the…
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.
These notes present an introduction to the method of geometric quantization. We discuss the main theorems in a style suitable for a theoretical physicist with an eye towards the physical motivation and the interpretation of the geometric…
Topological defects and operators give a far-reaching generalization of symmetries of quantum fields. An auxiliary topological field theory in one dimension higher than the QFT of interest, known as the SymTFT, provides a natural way for…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…
Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in…
Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short note we refine the meaning of qubits within the framework…
This Editorial introduces the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" which includes a number of research and review articles covering results in the group field theory (GFT) formalism for…
We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…
It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts…