14,553 research outputs found
Validity and failure of some entropy inequalities for CAR systems
Basic properties of von Neumann entropy such as the triangle inequality and
what we call MONO-SSA are studied for CAR systems.
We show that both inequalities hold for any even state. We construct a
certain class of noneven states giving counter examples of those inequalities.
It is not always possible to extend a set of prepared states on disjoint
regions to some joint state on the whole region for CAR systems.
However, for every even state, we have its `symmetric purification' by which
the validity of those inequalities is shown.
Some (realized) noneven states have peculiar state correlations among
subsystems and induce the failure of those inequalities.Comment: 14 pages, latex, to appear in JMP. Some typos are correcte
Non-formality of the odd dimensional framed little balls operads
We prove that the chain operad of the framed little balls (or disks) operad
is not formal as a non-symmetric operad over the rationals if the dimension of
their balls is odd and greater than 4.Comment: 10 pages, presentation improved, errors collected, references adde
Rational homotopy theory and differential graded category
We propose a generalization of Sullivan's de Rham homotopy theory to
non-simply connected spaces. The formulation is such that the real homotopy
type of a manifold should be the closed tensor dg-category of flat bundles on
it much the same as the real homotopy type of a simply connected manifold is
the de Rham algebra in original Sullivan's theory. We prove the existence of a
model category structure on the category of small closed tensor dg-categories
and as a most simple case, confirm an equivalence between the homotopy category
of spaces whose fundamental groups are finite and whose higher homotopy groups
are finite dimensional rational vector spaces and the homotopy category of
small closed tensor dg-categories satisfying certain conditions.Comment: 28pages, revised version, title changed, to appear in JPA
On fermion grading symmetry
We consider the univalence superselection rule. One would say perhaps ``There
is no indication in nature to invalidate this rule. Fermions do not
condensate!'' To explain our motivation, let us recall the correspondence of
fermion systems and Pauli systems by the Jordan-Wigner transformation. For a
finite lattice, fermion grading symmetry corresponds to the Pauli grading. For
an infinite lattice, the Pauli-grading can be spontaneously broken e.g. for the
XY-model. What is the status of the fermion grading? Nature tells that fermion
grading symmmetry cannot be broken for any physical model. But it seems that
its rigorous support is needed.Comment: A revised versio
On quasi-free dynamics on the resolvent algebra
The resolvent algebra is a new C*-algebra of the canonical commutation
relations of a boson field given by Buchholz-Grundling. We study analytic
properties of quasi-free dynamics on the resolvent algebra. Subsequently we
consider a supersymmetric quasi-free dynamics on the graded C*-algebra made of
a Clifford (fermion) algebra and a resolvent (boson) algebra. We establish an
infinitesimal supersymmetry formula upon the GNS Hilbert space for any regular
state satisfying some mild requirement which is standard in quantum field
theory. We assert that the supersymmetric dynamics is given as a C*-dynamics.Comment: This paper has been withdrawn by the author due to its being based on
some unjustified assumptions. Also there are mathematically incorrect
arguments that stem from the assumption
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