156 research outputs found
The shuffle Hopf algebra and quasiplanar Wick products
The operator valued distributions which arise in quantum field theory on the
noncommutative Minkowski space can be symbolized by a generalization of chord
diagrams, the dotted chord diagrams. In this framework, the combinatorial
aspects of quasiplanar Wick products are understood in terms of the shuffle
Hopf algebra of dotted chord diagrams, leading to an algebraic characterization
of quasiplanar Wick products as a convolution. Moreover, it is shown that the
distributions do not provide a weight system for universal knot invariants.Comment: 16 pages, prepared for the conference proceedings "Non commutative
Geometry and Physics", Laboratoire de physique th\'eorique d'Orsay, April
23-27, 200
Unitary Quantum Field Theory on the Noncommutative Minkowski space
This is the written version of a talk I gave at the 35th Symposium Ahrenshoop
in Berlin, Germany, August 2002. It is an exposition of joint work with S.
Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity
found in quantum field theory on noncommutative spacetimes in the context of
the so-called modified Feynman rules is linked to the notion of time ordering
implicitely used in the assumption that perturbation theory may be done in
terms of Feynman propagators. Two alternative approaches which do not entail a
violation of unitarity are sketched. An outlook upon our more recent work is
given.Comment: 6 pages. To appear in the proceedings of 35th International Symposium
Ahrenshoop on the theory of Elementary Particles: Recent Developments in
String / M Theory and Field Theory, Berlin, Germany, 26-30 Aug 2002 (special
issue of the journal "Fortschritte der Physik") v2: minor addition to the
abstrac
UV Finite Field Theories on Noncommutative Spacetimes: the Quantum Wick Product and Time Independent Perturbation Theory
In this article an energy correction is calculated in the time independent
perturbation setup using a regularised ultraviolet finite Hamiltonian on the
noncommutative Minkowski space. The correction to the energy is invariant under
rotation and translation but is not Lorentz covariant and this leads to a
distortion of the dispersion relation. In the limit where the noncommutativity
vanishes the common quantum field theory on the commutative Minkowski space is
reobtained.Comment: 8 pages, 2 figure
Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
We discuss a formulation of quantum field theory on quantum space time where
the perturbation expansion of the S-matrix is term by term ultraviolet finite.
The characteristic feature of our approach is a quantum version of the Wick
product at coinciding points: the differences of coordinates q_j - q_k are not
set equal to zero, which would violate the commutation relation between their
components. We show that the optimal degree of approximate coincidence can be
defined by the evaluation of a conditional expectation which replaces each
function of q_j - q_k by its expectation value in optimally localized states,
while leaving the mean coordinates (q_1 + ... + q_n)/n invariant.
The resulting procedure is to a large extent unique, and is invariant under
translations and rotations, but violates Lorentz invariance. Indeed, optimal
localization refers to a specific Lorentz frame, where the electric and
magnetic parts of the commutator of the coordinates have to coincide *).
Employing an adiabatic switching, we show that the S-matrix is term by term
finite. The matrix elements of the transfer matrix are determined, at each
order in the perturbative expansion, by kernels with Gaussian decay in the
Planck scale. The adiabatic limit and the large scale limit of this theory will
be studied elsewhere.
--
*) S. Doplicher, K. Fredenhagen, and J.E.Roberts, Commun. Math. Phys. 172,
187 (1995) [arXiv:hep-th/0303037]Comment: LaTeX (using amsmath, amssymb), 23 pages, 1 figure. Dedicated to
Rudolf Haag on the occasion of his 80th birthday. See also: hep-th/0303037,
hep-th/0201222. Second version: minor changes in exposition, two references
added. To appear on Commun. Math. Phy
Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
We give a definition of admissible counterterms appropriate for massive
quantum field theories on the noncommutative Minkowski space, based on a
suitable notion of locality. We then define products of fields of arbitrary
order, the so-called quasiplanar Wick products, by subtracting only such
admissible counterterms. We derive the analogue of Wick's theorem and comment
on the consequences of using quasiplanar Wick products in the perturbative
expansion.Comment: 22 pages, 2 figures, v2: minor changes, v3: minor changes, reference
adde
Perturbative quantization of two-dimensional space-time noncommutative QED
Using the method of perturbative quantization in the first order
approximation, we quantize a non-local QED-like theory including fermions and
bosons whose interactions are described by terms containing higher order
space-time derivatives. As an example, the two-dimensional space-time
noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,\theta^3),
where e is the NC-QED coupling constant and \theta is the noncommutativity
parameter. The resulting modified Lagrangian density is shown to include terms
consisting of first order time-derivative and higher order space-derivatives of
the modified field variables that satisfy the ordinary equal-time commutation
relations up to O(e^2,\theta^3. Using these commutation relations, the
canonical current algebra of the modified theory is also derived.Comment: 22 pages, no figure
DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
We discuss the perturbative approach a` la Dyson to a quantum field theory
with nonlocal self-interaction :phi*...*phi:, according to Doplicher,
Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction
of non locally time--ordered products of Wick monomials can be performed as
usual, and we discuss a very simple Dyson diagram.Comment: 15 pages, pdf has active hyperlinks. To appear in the proceedings of
the conference on "Rigorous quantum Field Theory", held at Saclay on July
19-21, 2004, on the occasion of Jacques Bros' 70th birthda
Quantum Field Theory on Quantum Spacetime
Condensed account of the Lectures delivered at the Meeting on {\it
Noncommutative Geometry in Field and String Theory}, Corfu, September 18 - 20,
2005.Comment: 10 page
Infrared cutoffs and the adiabatic limit in noncommutative spacetime
We discuss appropriate infrared cutoffs and their adiabatic limit for field
theories on the noncommutative Minkowski space in the Yang-Feldman formalism.
In order to do this, we consider a mass term as interaction term. We show that
an infrared cutoff can be defined quite analogously to the commutative case and
that the adiabatic limit of the two-point function exists and coincides with
the expectation, to all orders.Comment: 19 page
- …