Related papers: On Haag's theorem and renormalization ambiguities
The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
Classical results of the axiomatic quantum field theory, namely the irreducibility of the set of field operators, Reeh and Schlieder's theorems and generalized Haag's theorem, are proven in $SO(1,1)$ invariant quantum field theory, of which…
~It is shown that the quantum massive non-Abelian field theory established in the former papers is renormalizable. This conclusion is achieved with the aid of the Ward-Takahashi identities satisfied by the generating functionals which were…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
A simple introduction of renormalization in quantum field theory is discussed. Explanation of concepts is emphasized instead of the technical details.
In the perturbative approach to quantum field theory it is common to replace the propagator $i (p^{2}-m_{0}^{2}+i\varepsilon )^{-1}$ for a scalar field by a similar expression, namely $iZ (p^{2}-m^{2}+i\varepsilon )^{-1}$, where the shift…
We address the question of whether the quantum scale-invariant theories introduced in [1] are renormalizable or play the role of effective field theories that are valid below the Planck scale $M_P$. We show that starting from two-loop level…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry…
We discuss an alternative method to mass renormalize a quantum field Hamiltonian based on a requirement that the vacuum and single-particle sectors are not self-scattering. We illustrate the feasibility of this method for the concrete…
We review two different noncommutative gauge models generalizing approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called ``soft…
We give a simplified proof for the perturbative renormalizability of theories with massive vector particles. For renormalizability it is sufficient that the vector particle is treated as an gauge field, corresponding to an Abelian gauge…
The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.
We discuss the applicability of gamma_5-dependent field renormalization as a means of renormalizing away the apparent violation of Hara's theorem observed in the quark model. It is pointed out that a result totally analogous to the…