26 research outputs found
Field theories on spaces with linear fuzziness
A noncommutative space is considered the position operators of which satisfy
the commutativity relations of a Lie algebra. The basic tools for calculation
on this space, including the product of the fields, inner product and the
proper measure for integration are derived. Some general aspects of
perturbative field theory calculations on this space are also discussed. Among
the features of such models is that they are free from ultraviolet divergences
(and hence free from UV/IR mixing as well), if the group is compact. The
example of the group SO(3) or SU(2) is investigated in more detail.Comment: 12 pages, no figs., LaTeX. v2: Comments and discussions are added,
e.g. on absence of UV/IR phenomena. No change in result
On The Interaction Of D0-Brane Bound States And RR Photons
We consider the problem of the interaction between D0-brane bound state and
1-form RR photons by the world-line theory. Based on the fact that in the
world-line theory the RR gauge fields depend on the matrix coordinates of
D0-branes, the gauge fields also appear as matrices in the formulation. At the
classical level, we derive the Lorentz-like equations of motion for D0-branes,
and it is observed that the center-of-mass is colourless with respect to the
SU(N) sector of the background. Using the path integral method, the
perturbation theory for the interaction between the bound state and the RR
background is developed. We discuss what kind of field theory may be
corresponded to the amplitudes which are calculated by the perturbation
expansion in world-line theory. Qualitative considerations show that the
possibility of existence of a map between the world-line theory and the
non-Abelian gauge theory is very considerable.Comment: LaTeX, 28 pages, 4 eps figures. v2 and v3: eqs. (3.18) and (B.2) are
corrected, very small change
TeV-photon paradox and space with SU(2) fuzziness
The possibility is examined that a model based on space noncommutativity of
linear type can explain why photons from distant sources with multi-TeV
energies can reach earth. In particular within a model in which space
coordinates satisfy the algebra of SU(2) Lie group, it is shown that there is
the possibility that the pair production through the reaction of CMB and
energetic photons would be forbidden kinematically.Comment: 11 pages, no fig., LaTe
Do Quarks Obey D-Brane Dynamics?
The potential between two D0-branes at rest is calculated to be a linear.
Also the potential between two fast decaying D0-branes is found in agreement
with phenomenological heavy-quark potentials.Comment: 7 pages, no figures, LaTe
Dirac theory on a space with linear Lie type fuzziness
A spinor theory on a space with linear Lie type noncommutativity among
spatial coordinates is presented. The model is based on the Fourier space
corresponding to spatial coordinates, as this Fourier space is commutative.
When the group is compact, the real space exhibits lattice characteristics (as
the eigenvalues of space operators are discrete), and the similarity of such a
\emph{lattice} with ordinary lattices is manifested, among other things, in a
phenomenon resembling the famous \emph{fermion doubling} problem. A projection
is introduced to make the dynamical number of spinors equal to that
corresponding to the ordinary space. The actions for free and interacting
spinors (with Fermi-like interactions) are presented. The Feynman rules are
extracted and 1-loop corrections are investigated.Comment: 1+14 pages, no figure
Multispecies reaction-diffusion systems
Multispecies reaction-diffusion systems, for which the time evolution
equation of correlation functions become a closed set, are considered. A formal
solution for the average densities is found. Some special interactions and the
exact time dependence of the average densities in these cases are also studied.
For the general case, the large time behaviour of the average densities has
also been obtained.Comment: LaTeX file, 15 pages, to appear in Phys. Rev.
Quantum mechanics on space with SU(2) fuzziness
Quantum mechanics of models is considered which are constructed in spaces
with Lie algebra type commutation relations between spatial coordinates. The
case is specialized to that of the group SU(2), for which the formulation of
the problem via the Euler parameterization is also presented. SU(2)-invariant
systems are discussed, and the corresponding eigenvalue problem for the
Hamiltonian is reduced to an ordinary differential equation, as it is the case
with such models on commutative spaces.Comment: 12 pages, no figs, LaTe