26 research outputs found
Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing
We show that the Ultraviolet/Infrared mixing of noncommutative field theories
with the Gronewold-Moyal product, whereby some (but not all) ultraviolet
divergences become infrared, is a generic feature of translationally invariant
associative products. We find, with an explicit calculation that the phase
appearing in the nonplanar diagrams is the one given by the commutator of the
coordinates, the semiclassical Poisson structure of the non commutative
spacetime. We do this with an explicit calculation for represented generic
products.Comment: 24 pages, 1 figur
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
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
Physically motivated uncertainty relations at the Planck length for an emergent non commutative spacetime
We derive new space-time uncertainty relations (STUR) at the fundamental
Planck length from quantum mechanics and general relativity (GR), both in
flat and curved backgrounds. Contrary to claims present in the literature, our
approach suggests that no minimal uncertainty appears for lengths, but instead
for minimal space and four-volumes. Moreover, we derive a maximal absolute
value for the energy density. Finally, some considerations on possible
commutators among quantum operators implying our STUR are done.Comment: Final version published in "Class. Quantum Grav.
Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
We introduce the free quantum noncommutative fields as described by braided
tensor products. The multiplication of such fields is decomposed into three
operations, describing the multiplication in the algebra M of functions on
noncommutative space-time, the product in the algebra H of deformed field
oscillators, and the braiding by factor Psi_{M,H} between algebras M and H. For
noncommutativity generated by the twist factor we shall employ the star-product
realizations of the algebra M in terms of functions on standard Minkowski
space. The covariance of single noncommutative quantum fields under deformed
Poincare symmetries is described by the algebraic covariance conditions which
are equivalent to the deformation of generalized Heisenberg equations on
Poincare group manifold. We shall calculate the covariant braided field
commutator, which for free quantum noncommutative fields provides the field
quantization condition and is given by standard Pauli-Jordan function. For
ilustration of our new scheme we present explicit calculations for the
well-known case in the literature of canonically deformed free quantum fields.Comment: 19 pages, v.4, final versio