7,905 research outputs found
Noncommutative QFT and Renormalization
Field theories on deformed spaces suffer from the IR/UV mixing and
renormalization is generically spoiled. In work with R. Wulkenhaar, one of us
realized a way to cure this disease by adding one more marginal operator. We
review these ideas, show the application to models and use the heat
kernel expansion methods for a scalar field theory coupled to an external gauge
field on a -deformed space and derive noncommutative gauge field
actions.Comment: To appear in the proceedings of the Workshop "Noncommutative Geometry
in Field and String Theory", Corfu, 2005 (Greece
Induced Gauge Theory on a Noncommutative Space
We consider a scalar theory on canonically deformed Euclidean space
in 4 dimensions with an additional oscillator potential. This model is known to
be renormalisable. An exterior gauge field is coupled in a gauge invariant
manner to the scalar field. We extract the dynamics for the gauge field from
the divergent terms of the 1-loop effective action using a matrix basis and
propose an action for the noncommutative gauge theory, which is a candidate for
a renormalisable model.Comment: Typos corrected, one reference added; eqn. (49) corrected, one
equation number added; 30 page
Two and Three Loops Beta Function of Non Commutative Theory
The simplest non commutative renormalizable field theory, the
model on four dimensional Moyal space with harmonic potential is asymptotically
safe at one loop, as shown by H. Grosse and R. Wulkenhaar. We extend this
result up to three loops. If this remains true at any loop, it should allow a
full non perturbative construction of this model.Comment: 24 pages, 7 figure
Induced Gauge Theory on a Noncommutative Space
We discuss the calculation of the 1-loop effective action on four
dimensional, canonically deformed Euclidean space. The theory under
consideration is a scalar model with an additional oscillator
potential. This model is known to be re normalisable. Furthermore, we couple an
exterior gauge field to the scalar field and extract the dynamics for the gauge
field from the divergent terms of the 1-loop effective action using a matrix
basis. This results in proposing an action for noncommutative gauge theory,
which is a candidate for a renormalisable model.Comment: 8 page
Renormalisation of \phi^4-theory on noncommutative R^4 to all orders
We present the main ideas and techniques of the proof that the
duality-covariant four-dimensional noncommutative \phi^4-model is
renormalisable to all orders. This includes the reformulation as a dynamical
matrix model, the solution of the free theory by orthogonal polynomials as well
as the renormalisation by flow equations involving power-counting theorems for
ribbon graphs drawn on Riemann surfaces.Comment: 12 pages, 14 figures, LaTe
Noncommutative Induced Gauge Theories on Moyal Spaces
Noncommutative field theories on Moyal spaces can be conveniently handled
within a framework of noncommutative geometry. Several renormalisable matter
field theories that are now identified are briefly reviewed. The construction
of renormalisable gauge theories on these noncommutative Moyal spaces, which
remains so far a challenging problem, is then closely examined. The computation
in 4-D of the one-loop effective gauge theory generated from the integration
over a scalar field appearing in a renormalisable theory minimally coupled to
an external gauge potential is presented. The gauge invariant effective action
is found to involve, beyond the expected noncommutative version of the pure
Yang-Mills action, additional terms that may be interpreted as the gauge theory
counterpart of the harmonic term, which for the noncommutative -theory
on Moyal space ensures renormalisability. A class of possible candidates for
renormalisable gauge theory actions defined on Moyal space is presented and
discussed.Comment: 24 pages, 6 figures. Talk given at the "International Conference on
Noncommutative Geometry and Physics", April 2007, Orsay (France). References
updated. To appear in J. Phys. Conf. Se
Mass-symmetry breaking in three-body ions
The ground-state energy of three-body ions evolves when the
like-charge constituents are given different masses. The comparison of
with the average of and
reveals a competition between the symmetric term and the
antisymmetric one. The former dominates in the Born--Oppenheimer regime such as
the (p,t,e) case, while the latter wins for H-like systems with two
negative light particles surrounding a heavy nucleus. A comparison is also made
with the case of baryons in simple quark models with flavour independence.Comment: 4 pages, 3 figure
One-loop functions of a translation-invariant renormalizable noncommutative scalar model
Recently, a new type of renormalizable scalar model on
the Moyal space was proved to be perturbatively renormalizable. It is
translation-invariant and introduces in the action a term. We
calculate here the and functions at one-loop level for this
model. The coupling constant function is proved to have the
same behaviour as the one of the model on the commutative
. The function of the new parameter is also
calculated. Some interpretation of these results are done.Comment: 13 pages, 3 figure
Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
In this paper we provide a new proof that the Grosse-Wulkenhaar
non-commutative scalar Phi^4_4 theory is renormalizable to all orders in
perturbation theory, and extend it to more general models with covariant
derivatives. Our proof relies solely on a multiscale analysis in x space. We
think this proof is simpler and could be more adapted to the future study of
these theories (in particular at the non-perturbative or constructive level).Comment: 32 pages, v2: correction of lemmas 3.1 and 3.2 with no consequence on
the main resul
Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
As is well-known, there exists a four parameter family of local interactions
in 1D. We interpret these parameters as coupling constants of delta-type
interactions which include different kinds of momentum dependent terms, and we
determine all cases leading to many-body systems of distinguishable particles
which are exactly solvable by the coordinate Bethe Ansatz. We find two such
families of systems, one with two independent coupling constants deforming the
well-known delta interaction model to non-identical particles, and the other
with a particular one-parameter combination of the delta- and (so-called)
delta-prime interaction. We also find that the model of non-identical particles
gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the
other model we write down explicit formulas for all eigenfunctions.Comment: 23 pages v2: references adde
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