31 research outputs found
Differential Renormalization of the Wess-Zumino Model
We apply the recently developed method of differential renormalization to the
Wess-Zumino model. From the explicit calculation of a finite, renormalized
effective action, the -function is computed to three loops and is found
to agree with previous existing results. As a further, nontrivial check of the
method, the Callan-Symanzik equations are also verified to that loop order.
Finally, we argue that differential renormalization presents advantages over
other superspace renormalization methods, in that it avoids both the
ambiguities inherent to supersymmetric regularization by dimensional reduction
(SRDR), and the complications of virtually all other supersymmetric regulators.Comment: 10 page
Differential Renormalization of Massive Quantum Field Theories
We extend the method of differential renormalization to massive quantum field
theories treating in particular \ph4-theory and QED. As in the massless case,
the method proves to be simple and powerful, and we are able to find, in
particular, compact explicit coordinate space expressions for the finite parts
of two notably complicated diagrams, namely, the 2-loop 2-point function in
\ph4 and the 1-loop vertex in QED.Comment: 8 pages(LaTex, no figures
A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order
We develop a coordinate space renormalization of massless Quantum
Electrodynamics using the powerful method of differential renormalization. Bare
one-loop amplitudes are finite at non-coincident external points, but do not
accept a Fourier transform into momentum space. The method provides a
systematic procedure to obtain one-loop renormalized amplitudes with finite
Fourier transforms in strictly four dimensions without the appearance of
integrals or the use of a regulator. Higher loops are solved similarly by
renormalizing from the inner singularities outwards to the global one. We
compute all 1- and 2-loop 1PI diagrams, run renormalization group equations on
them and check Ward identities. The method furthermore allows us to discern a
particular pattern of renormalization under which certain amplitudes are seen
not to contain higher-loop leading logarithms. We finally present the
computation of the chiral triangle showing that differential renormalization
emerges as a natural scheme to tackle problems.Comment: 28 pages (figures not included
Gauge Invariant Geometric Variables For Yang-Mills Theory
In a previous publication [1], local gauge invariant geometric variables were
introduced to describe the physical Hilbert space of Yang-Mills theory. In
these variables, the electric energy involves the inverse of an operator which
can generically have zero modes, and thus its calculation is subtle. In the
present work, we resolve these subtleties by considering a small deformation in
the definition of these variables, which in the end is removed. The case of
spherical configurations of the gauge invariant variables is treated in detail,
as well as the inclusion of infinitely heavy point color sources, and the
expression for the associated electric field is found explicitly. These
spherical geometries are seen to correspond to the spatial components of
instanton configurations. The related geometries corresponding to Wu-Yang
monopoles and merons are also identified.Comment: 21 pp. in plain TeX. Uses harvmac.te
Two-Loop Beta Functions Without Feynman Diagrams
Starting from a consistency requirement between T-duality symmetry and
renormalization group flows, the two-loop metric beta function is found for a
d=2 bosonic sigma model on a generic, torsionless background. The result is
obtained without Feynman diagram calculations, and represents further evidence
that duality symmetry severely constrains renormalization flows.Comment: 4 pp., REVTeX. Added discussion on scheme (in)dependence; final
version to appear in Phys. Rev. Let