661 research outputs found
An Algebraic Criterion for the Ultraviolet Finiteness of Quantum Field Theories
An algebraic criterion for the vanishing of the beta function for
renormalizable quantum field theories is presented. Use is made of the descent
equations following from the Wess-Zumino consistency condition. In some cases,
these equations relate the fully quantized action to a local gauge invariant
polynomial. The vanishing of the anomalous dimension of this polynomial enables
us to establish a nonrenormalization theorem for the beta function ,
stating that if the one-loop order contribution vanishes, then will
vanish to all orders of perturbation theory. As a by-product, the special case
in which is only of one-loop order, without further corrections, is
also covered. The examples of the N=2,4 supersymmetric Yang-Mills theories are
worked out in detail.Comment: 1+32 pages, LaTeX2e, typos correcte
Nonstandard proof methods in toposes
We determine sufficient structure for an elementary topos to emulate E.
Nelson's Internal Set Theory in its internal language, and show that any topos
satisfying the internal axiom of choice occurs as a universe of standard
objects and maps. This development allows one to employ the proof methods of
nonstandard analysis (transfer, standardisation, and idealisation) in new
environments such as toposes of -sets and Boolean \'etendues
The phantom menace in representation theory
Our principal goal in this overview is to explain and motivate the concept of
a phantom in the representation theory of a finite dimensional algebra
. In particular, we exhibit the key role of phantoms towards
understanding how a full subcategory of the category
of all finitely generated left -modules is
embedded into , in terms of maps leaving or entering .
Contents: 1. Introduction and prerequisites; 2. Contravariant finiteness and
first examples; 3. Homological importance of contravariant finiteness and a
model application of the theory; 4. Phantoms. Definitions, existence, and basic
properties; 5. An application: Phantoms over string algebras
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