49 research outputs found
Almost product manifolds as the low energy geometry of Dirichlet branes
Any candidate theory of quantum gravity must address the breakdown of the
classical smooth manifold picture of space-time at distances comparable to the
Planck length. String theory, in contrast, is formulated on conventional
space-time. However, we show that in the low energy limit, the dynamics of
generally curved Dirichlet p-branes possess an extended local isometry group,
which can be absorbed into the brane geometry as an almost product structure.
The induced kinematics encode two invariant scales, namely a minimal length and
a maximal speed, without breaking general covariance. Quantum gravity effects
on D-branes at low energy are then seen to manifest themselves by the
kinematical effects of a maximal acceleration. Experimental and theoretical
implications of such new kinematics are easily derived. We comment on
consequences for brane world phenomenology.Comment: 12 pages, invited article in European Physical Journal C, reprinted
in Proceedings of the International School on Subnuclear Physics 2003 Erice
(World Scientific
How quantizable matter gravitates: a practitioner's guide
We present the practical step-by-step procedure for constructing canonical
gravitational dynamics and kinematics directly from any previously specified
quantizable classical matter dynamics, and then illustrate the application of
this recipe by way of two completely worked case studies. Following the same
procedure, any phenomenological proposal for fundamental matter dynamics must
be supplemented with a suitable gravity theory providing the coefficients and
kinematical interpretation of the matter equations, before any of the two
theories can be meaningfully compared to experimental data.Comment: 45 pages, no figure
All spacetimes beyond Einstein (Obergurgl Lectures)
Which geometries on a smooth manifold (apart from Lorentzian metrics) can
serve as a spacetime structure? This question is comprehensively addressed from
first principles in eight lectures, exploring the kinematics and gravitational
dynamics of all tensorial geometries on a smooth manifold that can carry
predictive matter equations, are time-orientable, and allow to distinguish
positive from negative particle energies.Comment: 44 pages, 7 figures, Lectures held for the Elitestudiengang Physik
Erlangen and Regensburg at Obergurgl/Austria, September 201
Geometry of physical dispersion relations
To serve as a dispersion relation, a cotangent bundle function must satisfy
three simple algebraic properties. These conditions are derived from the
inescapable physical requirements to have predictive matter field dynamics and
an observer-independent notion of positive energy. Possible modifications of
the standard relativistic dispersion relation are thereby severely restricted.
For instance, the dispersion relations associated with popular deformations of
Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9
figure
Brans-Dicke geometry
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by
unifying the metric and scalar field into a single geometric structure. Taking
this structure seriously as the geometry to which matter universally couples,
we show that the theory is fully consistent with solar system tests. This is in
striking constrast with the standard metric coupling, which grossly violates
post-Newtonian experimental constraints.Comment: 8 pages, v2 with additional comment and reference
Product structure of heat phase space and branching Brownian motion
A generical formalism for the discussion of Brownian processes with
non-constant particle number is developed, based on the observation that the
phase space of heat possesses a product structure that can be encoded in a
commutative unit ring. A single Brownian particle is discussed in a Hilbert
module theory, with the underlying ring structure seen to be intimately linked
to the non-differentiability of Brownian paths. Multi-particle systems with
interactions are explicitly constructed using a Fock space approach. The
resulting ring-valued quantum field theory is applied to binary branching
Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The
presented formalism permits the application of the full machinery of quantum
field theory to Brownian processes.Comment: 32 pages, journal version. Annals of Physics, N.Y. (to appear