2 research outputs found
Bi-local Fields in Noncommutative Field Theory
We propose a bi-local representation in noncommutative field theory. It
provides a simple description for high momentum degrees of freedom. It also
shows that the low momentum modes can be well approximated by ordinary local
fields. Long range interactions are generated in the effective action for the
lower momentum modes after integrating out the high momentum bi-local fields.
The low momentum modes can be represented by diagonal blocks in the matrix
model picture and the high momentum bi-local fields correspond to off-diagonal
blocks. This block-block interaction picture simply reproduces the infrared
singular behaviors of nonplanar diagrams in noncommutative field theory.Comment: 27 pages, 2 figure
Noncommutative Geometry Framework and The Feynman's Proof of Maxwell Equations
The main focus of the present work is to study the Feynman's proof of the
Maxwell equations using the NC geometry framework. To accomplish this task, we
consider two kinds of noncommutativity formulations going along the same lines
as Feynman's approach. This allows us to go beyond the standard case and
discover non-trivial results. In fact, while the first formulation gives rise
to the static Maxwell equations, the second formulation is based on the
following assumption
The results extracted from the second formulation are more significant since
they are associated to a non trivial -extension of the Bianchi-set of
Maxwell equations. We find and where
, , and are local functions depending on
the NC -parameter. The novelty of this proof in the NC space is
revealed notably at the level of the corrections brought to the previous
Maxwell equations. These corrections correspond essentially to the possibility
of existence of magnetic charges sources that we can associate to the magnetic
monopole since is not vanishing in general.Comment: LaTeX file, 16 page