152 research outputs found
Large Momentum bounds from Flow Equations
We analyse the large momentum behaviour of 4-dimensional massive euclidean
Phi-4-theory using the flow equations of Wilson's renormalization group. The
flow equations give access to a simple inductive proof of perturbative
renormalizability. By sharpening the induction hypothesis we prove new and, as
it seems, close to optimal bounds on the large momentum behaviour of the
correlation functions. The bounds are related to what is generally called
Weinberg's theorem.Comment: 14 page
Temperature Independent Renormalization of Finite Temperature Field Theory
We analyse 4-dimensional massive \vp^4 theory at finite temperature T in
the imaginary-time formalism. We present a rigorous proof that this quantum
field theory is renormalizable, to all orders of the loop expansion. Our main
point is to show that the counterterms can be chosen temperature independent,
so that the temperature flow of the relevant parameters as a function of
can be followed. Our result confirms the experience from explicit calculations
to the leading orders. The proof is based on flow equations, i.e. on the
(perturbative) Wilson renormalization group. In fact we will show that the
difference between the theories at T>0 and at T=0 contains no relevant terms.
Contrary to BPHZ type formalisms our approach permits to lay hand on
renormalization conditions and counterterms at the same time, since both appear
as boundary terms of the renormalization group flow. This is crucial for the
proof.Comment: 17 pages, typos and one footnote added, to appear in Ann.H.Poincar
The Surface counter-terms of the theory on the half space
In a previous work, we established perturbative renormalizability to all
orders of the massive -theory on a half-space also called the
semi-infinite massive -theory. Five counter-terms which are functions
depending on the position in the space, were needed to make the theory finite.
The aim of the present paper is to prove that these counter-terms are position
independent (i.e. constants) for a particular choice of renormalization
conditions. We investigate this problem by decomposing the correlation
functions into a bulk part, which is defined as the theory on the
full space with an interaction supported on the half-space, plus
a remainder which we call "the surface part". We analyse this surface part and
establish perturbatively that the theory in
is made finite by adding the bulk
counter-terms and two additional counter-terms to the bare interaction in the
case of Robin and Neumann boundary conditions. These surface counter-terms are
position independent and are proportional to and . For Dirichlet boundary conditions, we prove that no
surface counter-terms are needed and the bulk counter-terms are sufficient to
renormalize the connected amputated (Dirichlet) Schwinger functions. A key
technical novelty as compared to our previous work is a proof that the power
counting of the surface part of the correlation functions is better by one
power than their bulk counterparts.Comment: 59 page
Perturbative renormalization of theory on the half space with flow equations
In this paper, we give a rigorous proof of the renormalizability of the
massive theory on a half-space, using the renormalization group flow
equations. We find that five counter-terms are needed to make the theory
finite, namely , , ,
and for .
The amputated correlation functions are distributions in position space. We
consider a suitable class of test functions and prove inductive bounds for the
correlation functions folded with these test functions. The bounds are uniform
in the cutoff and thus directly lead to renormalizability.Comment: 35 page
Recent mathematical developments in quantum field theory
This workshop has focused on three areas in mathematical quantum field theory and their interrelations: 1) conformal field theory, 2) constructions of interacting models of quantum field theory by various methods, and 3) several approaches studying the interplay of quantum field theory and gravit
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