7,178 research outputs found
On Marshak's and Connes' views of chirality
I render the substance of the discussions I had with Robert E. Marshak
shortly before his death, wherein the kinship between the ``neutrino paradigm''
---espoused by Marshak--- and the central notion of K-cycle in noncommutative
geometry (NCG) was found. In that context, we give a brief account of the
Connes--Lott reconstruction of the Standard Model (SM).Comment: 10 pages, Plain Te
Improved Epstein-Glaser Renormalization II. Lorentz invariant framework
The Epstein--Glaser type T-subtraction introduced by one of the authors in a
previous paper is extended to the Lorentz invariant framework. The advantage of
using our subtraction instead of Epstein and Glaser's standard W-subtraction
method is especially important when working in Minkowski space, as then the
counterterms necessary to keep Lorentz invariance are simplified. We show how
T-renormalization of primitive diagrams in the Lorentz invariant framework
directly relates to causal Riesz distributions. A covariant subtraction rule in
momentum space is found, sharply improving upon the BPHZL method for massless
theories.Comment: LaTeX, 15 pages, no figure. Version to be published in J. Math. Phys.
(Section 7 on the Massive Case and some references have been withdrawn). To
the Memory of Laurent Schwart
Dynamics of a viscous vesicle in linear flows
An analytical theory is developed to describe the dynamics of a closed lipid
bilayer membrane (vesicle) freely suspended in a general linear flow.
Considering a nearly spherical shape, the solution to the creeping-flow
equations is obtained as a regular perturbation expansion in the excess area.
The analysis takes into account the membrane fluidity, incompressibility and
resistance to bending. The constraint for a fixed total area leads to a
non-linear shape evolution equation at leading order. As a result two regimes
of vesicle behavior, tank-treading and tumbling, are predicted depending on the
viscosity contrast between interior and exterior fluid. Below a critical
viscosity contrast, which depends on the excess area, the vesicle deforms into
a tank--treading ellipsoid, whose orientation angle with respect to the flow
direction is independent of the membrane bending rigidity. In the tumbling
regime, the vesicle exhibits periodic shape deformations with a frequency that
increases with the viscosity contrast. Non-Newtonian rheology such as normal
stresses is predicted for a dilute suspension of vesicles. The theory is in
good agreement with published experimental data for vesicle behavior in simple
shear flow
Quantum spherical spin models
A recently introduced class of quantum spherical spin models is considered in
detail. Since the spherical constraint already contains a kinetic part, the
Hamiltonian need not have kinetic term. As a consequence, situations with or
without momenta in the Hamiltonian can be described, which may lead to
different symmetry classes. Two models that show this difference are analyzed.
Both models are exactly solvable and their phase diagram is analyzed. A
transversal external field leads to a phase transition line that ends in a
quantum critical point. The two considered symmetries of the Hamiltonian
considered give different critical phenomena in the quantum critical region.
The model with momenta is argued to be analog to the large-N limit of an SU(N)
Heisenberg ferromagnet, and the model without momenta shares the critical
phenomena of an SU(N) Heisenberg antiferromagnet.Comment: 22 page
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