3 research outputs found
Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for
classical field theory presented in our previous publication, we construct in
this paper the Batalin-Vilkovisky complex in perturbatively renormalized
quantum field theory. The crucial technical ingredient is a proof that the
renormalized time-ordered product is equivalent to the pointwise product of
classical field theory. The renormalized Batalin-Vilkovisky algebra is then the
classical algebra but written in terms of the time-ordered product, together
with an operator which replaces the ill defined graded Laplacian of the
unrenormalized theory. We identify it with the anomaly term of the anomalous
Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we
do not refer to the path integral formalism and do not need to use
regularizations in intermediate steps.Comment: 34 page
The Algebra of Physical Observables in Nonlinearly Realized Gauge Theories
We classify the physical observables in spontaneously broken nonlinearly
realized gauge theories in the recently proposed loopwise expansion governed by
the Weak Power-Counting (WPC) and the Local Functional Equation. The latter
controls the non-trivial quantum deformation of the classical nonlinearly
realized gauge symmetry, to all orders in the loop expansion. The
Batalin-Vilkovisky (BV) formalism is used. We show that the dependence of the
vertex functional on the Goldstone fields is obtained via a canonical
transformation w.r.t. the BV bracket associated with the BRST symmetry of the
model. We also compare the WPC with strict power-counting renormalizability in
linearly realized gauge theories. In the case of the electroweak group we find
that the tree-level Weinberg relation still holds if power-counting
renormalizability is weakened to the WPC condition.Comment: 20 pages, 1 figur