Related papers: Algebraic Classical and Quantum Field Theory on Ca…
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…
P\"oschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties…
This report provides a brief review of recently developed extended framework for fundamental physics, designated as Quantum Field Mechanics and including causally complete and intrinsically unified theory of explicitly emerging elementary…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
In the framework of the QCD effective field theory called potential Non-Relativistic QCD, we explore quark-antiquark bound systems that may be dominated by the perturbative interaction and we discuss the extent of validity of such a…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
In the past decades, time ordered perturbation theory was very successful in describing relativistic scattering processes. It was developed for local quantum field theories. However, there are field theories which are governed by non-local…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
We introduce a new kind of foliated quantum field theory (FQFT) of gapped fracton orders in the continuum. FQFT is defined on a manifold with a layered structure given by one or more foliations, which each decompose spacetime into a stack…
We investigate various aspects of invariance under local symmetries in the framework of perturbative algebraic quantum field theory (pAQFT). Our main result is the proof that the quantum Batalin-Vilkovisky (BV) operator, on-shell, can be…
Quantization relates Poisson algebras to $C^*$-algebras. The analysis of local gauge symmetries in algebraic quantum field theory is approached through the quantization of classical gauge theories, regarded as constrained dynamical systems.…
I discuss some issues of perturbative quantum gravity, namely of a theory of self-interacting massless spin-2 quantum gauge fields, the gravitons, on flat space-time, in the framework of causal perturbation theory. The central aspects of…
This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes.…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in…