73 research outputs found
QED Fermi-Fields as Operator Valued Distributions and Anomalies
The treatment of fields as operator valued distributions (OPVD) is recalled
with the emphasis on the importance of causality following the work of Epstein
and Glaser. Gauge invariant theories demand the extension of the usual
translation operation on OPVD, thereby leading to a generalized
formulation. At D=2 the solvability of the Schwinger model is totally
preserved. At D=4 the paracompactness property of the Euclidean manifold
permits using test functions which are decomposition of unity and thereby
provides a natural justification and extension of the non perturbative heat
kernel method (Fujikawa) for abelian anomalies. On the Minkowski manifold the
specific role of causality in the restauration of gauge invariance (and mass
generation for ) is examplified in a simple way.Comment: soumis le 22/09/200
The Normality of Products Under Perfect Preimages
A proof of the following theorem is given, answering an open problem
attributed to Kunen: suppose that is compact and that is the image of
under a perfect map, is normal, and is normal. Then is normal
Pointfree pseudocompactness revisited
We give several internal and external characterizations of pseudocompactness in frames which extend (and transcend) analogous characterizations in topological spaces. In the case of internal characterizations we do not make reference (explicitly or implicitly) to the reals
UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited
Following Epstein-Glaser's work we show how a QFT formulation based on
operator valued distributions (OPVD) with adequate test functions treats
original singularities of propagators on the diagonal in a mathematically
rigourous way.Thereby UV and/or IR divergences are avoided at any stage, only a
finite renormalization finally occurs at a point related to the arbitrary scale
present in the test functions.Some well known UV cases are examplified.The
power of the IR treatment is shown for the free massive scalar field theory
developed in the (conventionally hopeless) mass perturbation expansion.It is
argued that the approach should prove most useful for non pertubative methods
where the usual determination of counterterms is elusiveComment: 6 pages 2 columns per pag
Leibnizian, Galilean and Newtonian structures of spacetime
The following three geometrical structures on a manifold are studied in
detail: (1) Leibnizian: a non-vanishing 1-form plus a Riemannian
metric \h on its annhilator vector bundle. In particular, the possible
dimensions of the automorphism group of a Leibnizian G-structure are
characterized. (2) Galilean: Leibnizian structure endowed with an affine
connection (gauge field) which parallelizes and \h. Fixed
any vector field of observers Z (), an explicit Koszul--type
formula which reconstruct bijectively all the possible 's from the
gravitational and vorticity fields
(plus eventually the torsion) is provided. (3) Newtonian: Galilean structure
with \h flat and a field of observers Z which is inertial (its flow preserves
the Leibnizian structure and ). Classical concepts in Newtonian
theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages
including a table, Late
- …