10,319 research outputs found

### Non-Commutative Geometry, Multiscalars, and the Symbol Map

Starting from the concept of the universal exterior algebra in
non-commutative differential geometry we construct differential forms on the
quantum phase-space of an arbitrary system. They bear the same natural
relationship to quantum dynamics which ordinary tensor fields have with respect
to classical hamiltonian dynamics.Comment: 8 pages, late

### Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation

The exact renormalization group equation for pure quantum gravity is used to
derive the non-perturbative \Fbeta-functions for the dimensionless Newton
constant and cosmological constant on the theory space spanned by the
Einstein-Hilbert truncation. The resulting coupled differential equations are
evaluated for a sharp cutoff function. The features of these flow equations are
compared to those found when using a smooth cutoff. The system of equations
with sharp cutoff is then solved numerically, deriving the complete
renormalization group flow of the Einstein-Hilbert truncation in $d=4$. The
resulting renormalization group trajectories are classified and their physical
relevance is discussed. The non-trivial fixed point which, if present in the
exact theory, might render Quantum Einstein Gravity nonperturbatively
renormalizable is investigated for various spacetime dimensionalities.Comment: 58 pages, latex, 24 figure

### On the Possibility of Quantum Gravity Effects at Astrophysical Scales

The nonperturbative renormalization group flow of Quantum Einstein Gravity
(QEG) is reviewed. It is argued that at large distances there could be strong
renormalization effects, including a scale dependence of Newton's constant,
which mimic the presence of dark matter at galactic and cosmological scales.Comment: LaTeX, 18 pages, 4 figures. Invited contribution to the Int. J. Mod.
Phys. D special issue on dark matter and dark energ

### A Proposal for a Differential Calculus in Quantum Mechanics

In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics,
we develop a {\it quantum-deformed} exterior calculus on the phase-space of an
arbitrary hamiltonian system. Introducing additional bosonic and fermionic
coordinates we construct a super-manifold which is closely related to the
tangent and cotangent bundle over phase-space. Scalar functions on the
super-manifold become equivalent to differential forms on the standard
phase-space. The algebra of these functions is equipped with a Moyal super-star
product which deforms the pointwise product of the classical tensor calculus.
We use the Moyal bracket algebra in order to derive a set of quantum-deformed
rules for the exterior derivative, Lie derivative, contraction, and similar
operations of the Cartan calculus.Comment: TeX file with phyzzx macro, 43 pages, no figure

- â€¦