790 research outputs found
Scalar Field Theory on Non-commutative Snyder Space-Time
We construct a scalar field theory on the Snyder non-commutative space-time.
The symmetry underlying the Snyder geometry is deformed at the co-algebraic
level only, while its Poincar\'e algebra is undeformed. The Lorentz sector is
undeformed at both algebraic and co-algebraic level, but the co-product for
momenta (defining the star-product) is non-co-associative. The Snyder-deformed
Poincar\'e group is described by a non-co-associative Hopf algebra. The
definition of the interacting theory in terms of a non-associative star-product
is thus questionable. We avoid the non-associativity by the use of a space-time
picture based on the concept of realization of a non-commutative geometry. The
two main results we obtain are: (i) the generic (namely for any realization)
construction of the co-algebraic sector underlying the Snyder geometry and (ii)
the definition of a non-ambiguous self interacting scalar field theory on this
space-time. The first order correction terms of the corresponding Lagrangian
are explicitly computed. The possibility to derive Noether charges for the
Snyder space-time is also discussed.Comment: 10 pages; v2: introduction rewritten, co-algebraic analysis improved,
references added; to appear in PR
Kappa-deformed Snyder spacetime
We present Lie-algebraic deformations of Minkowski space with undeformed
Poincare algebra. These deformations interpolate between Snyder and
kappa-Minkowski space. We find realizations of noncommutative coordinates in
terms of commutative coordinates and derivatives. Deformed Leibniz rule, the
coproduct structure and star product are found. Special cases, particularly
Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. Our
construction leads to a new class of deformed special relativity theories.Comment: 12 pages, no figures, LaTeX2e class file, accepted for publication in
Modern Physics Letters
Intermediate-statistics spin waves
In this paper, we show that spin waves, the elementary excitation of the
Heisenberg magnetic system, obey a kind of intermediate statistics with a
finite maximum occupation number n. We construct an operator realization for
the intermediate statistics obeyed by magnons, the quantized spin waves, and
then construct a corresponding intermediate-statistics realization for the
angular momentum algebra in terms of the creation and annihilation operators of
the magnons. In other words, instead of the Holstein-Primakoff representation,
a bosonic representation subject to a constraint on the occupation number, we
present an intermediate-statistics representation with no constraints. In this
realization, the maximum occupation number is naturally embodied in the
commutation relation of creation and annihilation operators, while the
Holstein-Primakoff representation is a bosonic operator relation with an
additional putting-in-by-hand restriction on the occupation number. We deduce
the intermediate-statistics distribution function for magnons. On the basis of
these results, we calculate the dispersion relations for ferromagnetic and
antiferromagnetic spin waves. The relations between the intermediate statistics
that magnons obey and the other two important kinds of intermediate statistics,
Haldane-Wu statistics and the fractional statistics of anyons, are discussed.
We also compare the spectrum of the intermediate-statistics spin wave with the
exact solution of the one-dimensional s = 1/2 Heisenberg model, which is
obtained by the Bethe ansatz method. For ferromagnets, we take the
contributions from the interaction between magnons (the quartic contribution),
the next-to-nearest neighbor interaction, and the dipolar interaction into
account for comparison with the experiment.Comment: 22 pages, 2 figure
Concentration-independent spontaneously forming biomimetric vesicles
In this Letter we present small-angle neutron scattering data from a biomimetic system composed of the phospholipids dimyristoyl and dihexanoyl phosphorylcholine (DMPC and DHPC, respectively). Doping DMPC-DHPC multilamellar vesicles with either the negatively charged lipid dimyristoyl phosphorylglycerol (DMPG, net charge -1) or the divalent cation, calcium (Ca2+), leads to the spontaneous formation of energetically stabilized monodisperse unilamellar vesicles whose radii are concentration independent and in contrast with previous experimental observations
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