101 research outputs found
Quantum Spacetime: a Disambiguation
We review an approach to non-commutative geometry, where models are
constructed by quantisation of the coordinates. In particular we focus on the
full DFR model and its irreducible components; the (arbitrary) restriction to a
particular irreducible component is often referred to as the "canonical quantum
spacetime". The aim is to distinguish and compare the approaches under various
points of view, including motivations, prescriptions for quantisation, the
choice of mathematical objects and concepts, approaches to dynamics and to
covariance.Comment: special issue of SIGMA "Noncommutative Spaces and Fields
Alien Registration- Piacitelli, Loreto (Portland, Cumberland County)
https://digitalmaine.com/alien_docs/25597/thumbnail.jp
Non Local Theories: New Rules for Old Diagrams
We show that a general variant of the Wick theorems can be used to reduce the
time ordered products in the Gell-Mann & Low formula for a certain class on non
local quantum field theories, including the case where the interaction
Lagrangian is defined in terms of twisted products.
The only necessary modification is the replacement of the
Stueckelberg-Feynman propagator by the general propagator (the ``contractor''
of Denk and Schweda)
D(y-y';tau-tau')= - i
(Delta_+(y-y')theta(tau-tau')+Delta_+(y'-y)theta(tau'-tau)), where the
violations of locality and causality are represented by the dependence of
tau,tau' on other points, besides those involved in the contraction. This leads
naturally to a diagrammatic expansion of the Gell-Mann & Low formula, in terms
of the same diagrams as in the local case, the only necessary modification
concerning the Feynman rules. The ordinary local theory is easily recovered as
a special case, and there is a one-to-one correspondence between the local and
non local contributions corresponding to the same diagrams, which is preserved
while performing the large scale limit of the theory.Comment: LaTeX, 14 pages, 1 figure. Uses hyperref. Symmetry factors added;
minor changes in the expositio
Alien Registration- Piacitelli, Loreto (Portland, Cumberland County)
https://digitalmaine.com/alien_docs/25598/thumbnail.jp
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
Quantum Spacetime and Algebraic Quantum Field Theory
We review the investigations on the quantum structure of spactime, to be
found at the Planck scale if one takes into account the operational limitations
to localization of events which result from the concurrence of Quantum
Mechanics and General Relativity. We also discuss the different approaches to
(perturbative) Quantum Field Theory on Quantum Spacetime, and some of the
possible cosmological consequences.Comment: 49 pages, 2 figure
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
Twisted Covariance and Weyl Quantisation
In this letter we wish to clarify in which sense the tensor nature of the
commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski
spacetime quantisation cannot be suppressed even in the twisted approach to
Lorentz covariance. We then address the vexata quaestio "why theta"?Comment: 6 pages, pdf has active hyperlinks Slight change in title. Appendix
added on more general coordinates for symbols. References added. To appear in
the Proceedings of the XXV Max Born Symposium, Wroclaw, June 29-July 3, 200
Any compact group is a gauge group
The assignment of local observables in the vacuum sector, fulfilling the
standard axioms of local quantum theory, is known to determine uniquely a
compact group G of gauge transformations of the first kind together with a
central involutive element k of G, and a complete normal algebra of fields
carrying the localizable charges, on which k defines the Bose/Fermi grading.
We show here that any such pair {G,k}, where G is compact metrizable, does
actually appear. The corresponding model can be chosen to fulfill also the
split property.
This is not a dynamical phenomenon: a given {G,k} arises as the gauge group
of a model where the local algebras of observables are a suitable subnet of
local algebras of a possibly infinite product of free field theories.Comment: 13 pages, LaTeX. To appear on Reviews in Mathematical Physics.
References added; minor changes in styl
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