41 research outputs found
Supercurrent and Local Coupling in the Wess-Zumino Model
We study the Wess-Zumino model with the coupling extended to a chiral
superfield. In order to incorporate the renormalization effects a further
external real field has to be introduced. It is then possible to derive a
Callan-Symanzik equation and to prove renormalizability. By constructing the
supercurrent in this context the whole machinery for describing the
superconformal symmetries becomes available. The presence of the external
fields allows also to define multiple insertions of all relevant composite
operators. Interesting relations to the curved superspace treatment show up.Comment: 16 page
Time-ordered Perturbation Theory on Noncommutative Spacetime: Basic Rules
Assuming the S-matrix on noncommutative (NC) spacetime can still be
developped perturbatively in terms of the time-ordered exponential of the
interaction Lagrangian, we investigate the perturbation theory of NC field
theory. We first work out with care some typical Green functions starting from
the usual concepts of time-ordering and commutation relations for free fields.
The results are found to be very different from those in the naive approach
pursued in the literature. A simple framework then appears naturally which can
incorporate the new features of our results and which turns out to be the usual
time-ordered perturbation theory extended to the NC context. We provide the
prescriptions for computing S-matrix elements and Green functions in this
framework. We also emphasize that the naive seemingly covariant approach cannot
be reproduced from the current one, in contrast to the field theory on ordinary
spacetime. We attribute this to the phase-like nonlocal interaction intrinsic
in NC field theory which modifies the analytic properties of Green functions
significantly.Comment: 19 pages, 1 figure using axodraw; version 2: typos fixed and one ref
updated, to appear in Eur Phys J
On Double Gauging of U(1) Symmetry on Noncommutative Space
We point out that a field \phi charged under a global U(1) symmetry generally
allows for a starred localized extension with the transformation rule, \phi\to
U_L\star\phi\star U_R^{-1}. This results in a double gauging of the global U(1)
symmetry on noncommutative space. We interpret the gauge theory so obtained in
terms of the gauge fields that in the commutative limit appear naturally and
are respectively the gauge field responsible for the charge and a decoupled
vector field. The interactions are shown to be very different from those
obtained by assigning a transformation rule of \phi\to U\star\phi or \phi\star
U^{-1}.Comment: 8 pages, no figure
Rigid invariance as derived from BRS invariance: The abelian Higgs model
Consequences of a symmetry, e.g.\ relations amongst Green functions, are
renormalization scheme independently expressed in terms of a rigid Ward
identity. The corresponding local version yields information on the respective
current. In the case of spontaneous breakdown one has to define the theory via
the BRS invariance and thus to construct rigid and current Ward identity
non-trivially in accordance with it. We performed this construction to all
orders of perturbation theory in the abelian Higgs model as a prelude to the
standard model. A technical tool of interest in itself is the use of a doublet
of external scalar ``background'' fields. The Callan-Symanzik equation has an
interesting form and follows easily once the rigid invariance is established.Comment: 33 pages, Plain Te