Related papers: An analyst's take on the BPHZ theorem
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
We implement the concept of Wilson renormalization in the context of simple quantum mechanical systems. The attractive inverse square potential leads to a $\b$ function with a nontrivial ultraviolet stable fixed point and the Hulthen…
We present the natural arguments for the rationality of a recently proposed simple approach for renormalization which is based solving differential equations. The renormalization group equation is also derived in a natural way and…
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV)…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
We present, in the context of dimensional regularization, a prescription to renormalize Feynman diagrams with an arbitrary number of external fermions. This prescription, which is based on the original t'Hooft-Veltman proposal to keep…
We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
A formalism is presented to express decoherence both in the markovian and nonmarkovian regimes and both dissipative and nondissipative in isolated systems. The main physical hypothesis, already contained in the literature, amounts to…
A definition is given, in the framework of stochastic quantization, for the dynamics of a system composed of classical and quantum degrees of freedom mutually interacting. It is found that the theory breaks reflection positivity, and hence…
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…
We present the proof of renormalization of the Horava theory, in the nonprojectable version. We obtain a form of the quantum action that exhibits a manifest BRST-symmetry structure. Previous analysis has shown that the divergences produced…
The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that,…
Hamiltonian Renormalisation, as defined within this series of works, was derived from covariant Wilson renormalisation via Osterwalder-Schrader reconstruction. As such it directly applies to QFT with a true (physical) Hamiltonian bounded…
We study the renormalization group flow in general quantum field theories with quenched disorder, focusing on random quantum critical points. We show that in disorder-averaged correlation functions the flow mixes local and non-local…
Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop…
We introduce a generalization of the Euclidean algorithm for rings equipped with an involution, and completely enumerate all isomorphism classes of orders over definite, rational quaternion algebras equipped with an orthogonal involution…