Related papers: Regularization and Anomalies in Gauge Theory
The Pauli--Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential…
We study renormalization effects in the Abelian Chern-Simons (CS) action. These effects can be non-trivial when the gauge field is coupled to dynamical matter, since the regularization of the UV divergences in the model forces the…
I point out two of the subtleties referred to in the title. The first is that gauge-invariant magnetic systems may realized under general circumstances, as suggested by a simple theorem. The second subtlety is that care is needed to…
We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization…
Dimensional regularization is arguably the most popular and efficient scheme for multi-loop calculations. Yet, when applied to chiral (gauge) theories like the Standard Model and its extensions, one is forced to deal with the infamous…
I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions…
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant…
We analyse the origin of the Adler anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge…
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at…
It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaume and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice…
In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is…
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and…
We investigate instabilities and their regularization in theories of gravitation. Instabilities can be beneficial since their growth often leads to prominent observable signatures which makes them especially relevant to relatively low…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…
We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed…
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
Consideration of the Noether variational problem for any theory whose action is invariant under global and/or local gauge transformations leads to three distinct theorems. These include the familiar Noether theorem, but also two equally…