38 research outputs found
On the Universality of Matrix Models for Random Surfaces
We present an alternative procedure to eliminate irregular contributions in
the perturbation expansion of c=0-matrix models representing the sum over
triangulations of random surfaces, thereby reproducing the results of Tutte [1]
and Brezin et al. [2] for the planar model. The advantage of this method is
that the universality of the critical exponents can be proven from general
features of the model alone without explicit determination of the free energy
and therefore allows for several straightforward generalizations including
cases with non-vanishing central charge c< 1.Comment: 9 pages, 3 figure
Dimension Theory of Graphs and Networks
Starting from the working hypothesis that both physics and the corresponding
mathematics have to be described by means of discrete concepts on the
Planck-scale, one of the many problems one has to face in this enterprise is to
find the discrete protoforms of the building blocks of continuum physics and
mathematics. A core concept is the notion of dimension. In the following we
develop such a notion for irregular structures like (large) graphs and networks
and derive a number of its properties. Among other things we show its stability
under a wide class of perturbations which is important if one has 'dimensional
phase transitions' in mind. Furthermore we systematically construct graphs with
almost arbitrary 'fractal dimension' which may be of some use in the context of
'dimensional renormalization' or statistical mechanics on irregular sets.Comment: 20 pages, 7 figures, LaTex2e, uses amsmath, amsfonts, amssymb,
latexsym, epsfi
Generalized Quantum Theory: Overview and Latest Developments
The main formal structures of Generalized Quantum Theory are summarized.
Recent progress has sharpened some of the concepts, in particular the notion of
an observable, the action of an observable on states (putting more emphasis on
the role of proposition observables), and the concept of generalized
entanglement. Furthermore, the active role of the observer in the structure of
observables and the partitioning of systems is emphasized.Comment: 14 pages, update in reference
Space-Time Noncommutative Field Theories And Unitarity
We study the perturbative unitarity of noncommutative scalar field theories.
Field theories with space-time noncommutativity do not have a unitary S-matrix.
Field theories with only space noncommutativity are perturbatively unitary.
This can be understood from string theory, since space noncommutative field
theories describe a low energy limit of string theory in a background magnetic
field. On the other hand, there is no regime in which space-time noncommutative
field theory is an appropriate description of string theory. Whenever
space-time noncommutative field theory becomes relevant massive open string
states cannot be neglected.Comment: 15 pages, 2 figures, harvmac; references adde
Proper time and Minkowski structure on causal graphs
For causal graphs we propose a definition of proper time which for small
scales is based on the concept of volume, while for large scales the usual
definition of length is applied. The scale where the change from "volume" to
"length" occurs is related to the size of a dynamical clock and defines a
natural cut-off for this type of clock. By changing the cut-off volume we may
probe the geometry of the causal graph on different scales and therey define a
continuum limit. This provides an alternative to the standard coarse graining
procedures. For regular causal lattice (like e.g. the 2-dim. light-cone
lattice) this concept can be proven to lead to a Minkowski structure. An
illustrative example of this approach is provided by the breather solutions of
the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure
Relational interpretation of the wave function and a possible way around Bell's theorem
The famous ``spooky action at a distance'' in the EPR-szenario is shown to be
a local interaction, once entanglement is interpreted as a kind of ``nearest
neighbor'' relation among quantum systems. Furthermore, the wave function
itself is interpreted as encoding the ``nearest neighbor'' relations between a
quantum system and spatial points. This interpretation becomes natural, if we
view space and distance in terms of relations among spatial points. Therefore,
``position'' becomes a purely relational concept. This relational picture leads
to a new perspective onto the quantum mechanical formalism, where many of the
``weird'' aspects, like the particle-wave duality, the non-locality of
entanglement, or the ``mystery'' of the double-slit experiment, disappear.
Furthermore, this picture cirumvents the restrictions set by Bell's
inequalities, i.e., a possible (realistic) hidden variable theory based on
these concepts can be local and at the same time reproduce the results of
quantum mechanics.Comment: Accepted for publication in "International Journal of Theoretical
Physics
Spectral action and big desert
The values of the Higgs mass are obtained for two possibilities of extending
the standard model in a way compatible with the existence of a noncommutative
structure at high energies. We assume the existence of a big desert between the
low energy electroweak scale and the high energy scale GeV, where noncommutative features become relevant. We conclude that
it is extremely difficult to depart from the Higgs mass value GeV obtained from noncommutative geometry for the standard
model with three generations only.Comment: 11 pages, 1 figure, 3 table
Epistemic Entanglement due to Non-Generating Partitions of Classical Dynamical Systems
Quantum entanglement relies on the fact that pure quantum states are
dispersive and often inseparable. Since pure classical states are
dispersion-free they are always separable and cannot be entangled. However,
entanglement is possible for epistemic, dispersive classical states. We show
how such epistemic entanglement arises for epistemic states of classical
dynamical systems based on phase space partitions that are not generating. We
compute epistemically entangled states for two coupled harmonic oscillators.Comment: 13 pages, no figures; International Journal of Theoretical Physics,
201
Signals for Non-Commutative Interactions at Linear Colliders
Recent theoretical results have demonstrated that non-commutative geometries
naturally appear within the context of string/M-theory. One consequence of this
possibility is that QED takes on a non-abelian nature due to the introduction
of 3- and 4-point functions. In addition, each QED vertex acquires a momentum
dependent phase factor. We parameterize the effects of non-commutative
space-time co-ordinates and show that they lead to observable signatures in
several QED processes in collisions. In particular, we
examine pair annihilation, Moller and Bhabha scattering, as well as
scattering and show that non-commutative scales
of order a TeV can be probed at high energy linear colliders.Comment: 51 pages, 23 figures, typos corrected, figure and references adde