652 research outputs found
Particle-like solutions to classical noncommutative gauge theory
We construct perturbative static solutions to the classical field equations
of noncommutative U(1) gauge theory for the three cases: a) space-time
noncommutativity, b) space-space noncommutativity and c) both a) and b). The
solutions tend to the Coulumb solution at spatial infinity and are valid for
intermediate values of the radial coordinate . They yield a self-charge in a
sphere of radius centered about the origin which increases with decreasing
for case a), and decreases with decreasing for case b). For case a)
this may mean that the exact solution screens an infinite charge at the origin,
while for case b) it is plausible that the charge density is well behaved at
the origin, as happens in Born-Infeld electrodynamics. For both cases a) and b)
the self-energy in the intermediate region grows faster as tends to the
origin than that of the Coulumb solution. It then appears that the divergence
of the classical self-energy is more severe in the noncommutative theory than
it is in the corresponding commutative theory. We compute the lowest order
effects of these solutions on the hydrogen atom spectrum and use them to put
experimental bounds on the space-time and space-space noncommutative scales. We
find that cases a) and b) have different experimental signatures.Comment: 21 page
Noncommuting spherical coordinates
Restricting the states of a charged particle to the lowest Landau level
introduces a noncommutativity between Cartesian coordinate operators. This idea
is extended to the motion of a charged particle on a sphere in the presence of
a magnetic monopole. Restricting the dynamics to the lowest energy level
results in noncommutativity for angular variables and to a definition of a
noncommuting spherical product. The values of the commutators of various
angular variables are not arbitrary but are restricted by the discrete
magnitude of the magnetic monopole charge. An algebra, isomorphic to angular
momentum, appears. This algebra is used to define a spherical star product.
Solutions are obtained for dynamics in the presence of additional angular
dependent potentials.Comment: 5 pages, RevTex4 fil
Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
In this paper we deal with the issue of Lorentz symmetry breaking in quantum
field theories formulated in a non-commutative space-time. We show that, unlike
in some recente analysis of quantum gravity effects, supersymmetry does not
protect the theory from the large Lorentz violating effects arising from the
loop corrections. We take advantage of the non-commutative Wess-Zumino model to
illustrate this point.Comment: 9 pages, revtex4. Corrected references. Version published in PR
Newton's law in an effective non commutative space-time
The Newtonian Potential is computed exactly in a theory that is fundamentally
Non Commutative in the space-time coordinates. When the dispersion for the
distribution of the source is minimal (i.e. it is equal to the non commutative
parameter ), the behavior for large and small distances is analyzed.Comment: 5 page
Gauge Theory of the Star Product
The choice of a star product realization for noncommutative field theory can
be regarded as a gauge choice in the space of all equivalent star products.
With the goal of having a gauge invariant treatment, we develop tools, such as
integration measures and covariant derivatives on this space. The covariant
derivative can be expressed in terms of connections in the usual way giving
rise to new degrees of freedom for noncommutative theories.Comment: 16 page
Star product formula of theta functions
As a noncommutative generalization of the addition formula of theta
functions, we construct a class of theta functions which are closed with
respect to the Moyal star product of a fixed noncommutative parameter. These
theta functions can be regarded as bases of the space of holomorphic
homomorphisms between holomorphic line bundles over noncommutative complex
tori.Comment: 12 page
Noncommutative differential calculus for Moyal subalgebras
We build a differential calculus for subalgebras of the Moyal algebra on R^4
starting from a redundant differential calculus on the Moyal algebra, which is
suitable for reduction. In some cases we find a frame of 1-forms which allows
to realize the complex of forms as a tensor product of the noncommutative
subalgebras with the external algebra Lambda^*.Comment: 13 pages, no figures. One reference added, minor correction
Phenomenology of Noncommutative Field Theories
Experimental limits on the violation of four-dimensional Lorentz invariance
imply that noncommutativity among ordinary spacetime dimensions must be small.
In this talk, I review the most stringent bounds on noncommutative field
theories and suggest a possible means of evading them: noncommutativity may be
restricted to extra, compactified spatial dimensions. Such theories have a
number of interesting features, including Abelian gauge fields whose
Kaluza-Klein excitations have self couplings. We consider six-dimensional QED
in a noncommutative bulk, and discuss the collider signatures of the model.Comment: 7 pages RevTeX, 4 eps figures, Invited plenary talk, IX Mexican
Workshop on Particles and Fields, November 17-22, 2003, Universidad de
Colima, Mexic
Physical Wigner functions
In spite of their potential usefulness, the characterizations of Wigner
functions for Bose and Fermi statistics given by O'Connell and Wigner himself
almost thirty years ago has drawn little attention. With an eye towards
applications in quantum chemistry, we revisit and reformulate them in a more
convenient way.Comment: Latex, 10 page
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
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