9,287 research outputs found
The Luttinger-Schwinger Model
We study the Luttinger-Schwinger model, i.e. the (1+1) dimensional model of
massless Dirac fermions with a non-local 4-point interaction coupled to a
U(1)-gauge field. The complete solution of the model is found using the
boson-fermion correspondence, and the formalism for calculating all gauge
invariant Green functions is provided. We discuss the role of anomalies and
show how the existence of large gauge transformations implies a fermion
condensate in all physical states. The meaning of regularization and
renormalization in our well-defined Hilbert space setting is discussed. We
illustrate the latter by performing the limit to the Thirring-Schwinger model
where the interaction becomes local.Comment: 19 pages, Latex, to appear in Annals of Physics, download problems
fixe
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 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
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
Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base
As a first application of our renormalisation group approach to non-local
matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean
two-dimensional noncommutative \phi^4-theory. It is widely believed that this
model is renormalisable in momentum space arguing that there would be
logarithmic UV/IR-divergences only. Although momentum space Feynman graphs can
indeed be computed to any loop order, the logarithmic UV/IR-divergence appears
in the renormalised two-point function -- a hint that the renormalisation is
not completed. In particular, it is impossible to define the squared mass as
the value of the two-point function at vanishing momentum. In contrast, in our
matrix approach the renormalised N-point functions are bounded everywhere and
nevertheless rely on adjusting the mass only. We achieve this by introducing
into the cut-off model a translation-invariance breaking regulator which is
scaled to zero with the removal of the cut-off. The naive treatment without
regulator would not lead to a renormalised theory.Comment: 26 pages, 44 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
Geometry of the Grosse-Wulkenhaar Model
We define a two-dimensional noncommutative space as a limit of finite-matrix
spaces which have space-time dimension three. We show that on such space the
Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the
action for the scalar field coupled to the curvature. We also discuss a natural
generalization to four dimensions.Comment: 16 pages, version accepted in JHE
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
UV/IR duality in noncommutative quantum field theory
We review the construction of renormalizable noncommutative euclidean
phi(4)-theories based on the UV/IR duality covariant modification of the
standard field theory, and how the formalism can be extended to scalar field
theories defined on noncommutative Minkowski space.Comment: 12 pages; v2: minor corrections, note and references added;
Contribution to proceedings of the 2nd School on "Quantum Gravity and Quantum
Geometry" session of the 9th Hellenic School on Elementary Particle Physics
and Gravity, Corfu, Greece, September 13-20 2009. To be published in General
Relativity and Gravitatio
Two Color Entanglement
We report on the generation of entangled states of light between the
wavelengths 810 and 1550 nm in the continuous variable regime. The fields were
produced by type I optical parametric oscillation in a standing-wave cavity
build around a periodically poled potassium titanyl phosphate crystal, operated
above threshold. Balanced homodyne detection was used to detect the
non-classical noise properties, while filter cavities provided the local
oscillators by separating carrier fields from the entangled sidebands. We were
able to obtain an inseparability of I=0.82, corresponding to about -0.86 dB of
non-classical quadrature correlation.Comment: 4 pages, 2 figure
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