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An effective quantum field theory (QFT) with a manifest UV/IR connection, so as to be valid for arbitrarily large volumes, can successfully be applied to the cosmological dark energy problem as well as the cosmological constant (CC)…
We formulate quantum field theory in triangulated spacetime using compositional quantum field theory and tensor network methods. We show that gravitational interactions emerge as a low-energy effective phenomenon in this framework. For…
In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
An algebraic system is introduced, which is very useful for doing scattering calculations in quantum field theory. It is the set of all real numbers greater than or equal to -m^2 with parity designation and a special rule for addition and…
This chapter provides a non-technical overview and motivation for the recent interactions between algebraic quantum field theory (AQFT) and rather abstract mathematical disciplines such as operads, model categories and higher categories.
We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural…
By extending the method developed in our recent paper \cite{LM} we present the AQFT framework in terms of von Neumann algebras. In particular, this approach allows for a locally covariant categorical description of AQFT which moreover…
Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical…
The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which…
Motivated by hints of the effective emergent nature of spacetime structure, we formulate a spacetime-free algebraic framework for quantum theory, in which no a priori background geometric structure is required. Such a framework is necessary…
Quantum technology is full of figurative and literal noise obscuring its promise. In this overview, we will attempt to provide a sober assessment of the promise of quantum technology with a focus on computing. We provide a tour of quantum…
The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section-titles (with new sections indicated with stars) are: Introduction and preliminaries, Construction…
Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial…
Quantum computing is a technology that promises to offer significant advantages during the coming decades. Though the technology is still in a prototype stage, the last few years have seen many of these prototype devices become accessible…
The GIREP community on teaching and learning quantum physics and the Education section of the Quantum flagship project of the European Union (QTEdu) have brought together different stakeholders in the field of teaching quantum physics on…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…