39,642 research outputs found
Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that
has at least one negative real eigenvalue is necessarily indefinite. We
introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras
and provide a pair of basic realizations of the algebra of N=2
pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is
identified with either a boson-phermion or a boson-abnormal-phermion exchange
symmetry. We further establish the physical equivalence (non-equivalence) of
phermions (abnormal phermions) with ordinary fermions, describe the underlying
Lie algebras, and study multi-particle systems of abnormal phermions. The
latter provides a certain bosonization of multi-fermion systems.Comment: 20 pages, to appear in J.Phys.
Diffeological Clifford algebras and pseudo-bundles of Clifford modules
We consider the diffeological version of the Clifford algebra of a
(diffeological) finite-dimensional vector space; we start by commenting on the
notion of a diffeological algebra (which is the expected analogue of the usual
one) and that of a diffeological module (also an expected counterpart of the
usual notion). After considering the natural diffeology of the Clifford
algebra, and its expected properties, we turn to our main interest, which is
constructing pseudo-bundles of diffeological Clifford algebras and those of
diffeological Clifford modules, by means of the procedure called diffeological
gluing. The paper has a significant expository portion, regarding mostly
diffeological algebras and diffeological vector pseudo-bundles.Comment: 35 pages; exposition improved, an example adde
The Geometry of Border Bases
The main topic of the paper is the construction of various explicit flat
families of border bases. To begin with, we cover the punctual Hilbert scheme
Hilb^\mu(A^n) by border basis schemes and work out the base changes. This
enables us to control flat families obtained by linear changes of coordinates.
Next we provide an explicit construction of the principal component of the
border basis scheme, and we use it to find flat families of maximal dimension
at each radical point. Finally, we connect radical points to each other and to
the monomial point via explicit flat families on the principal component
The DG-category of secondary cohomology operations
We study track categories (i.e., groupoid-enriched categories) endowed with
additive structure similar to that of a 1-truncated DG-category, except that
composition is not assumed right linear. We show that if such a track category
is right linear up to suitably coherent correction tracks, then it is weakly
equivalent to a 1-truncated DG-category. This generalizes work of the first
author on the strictification of secondary cohomology operations. As an
application, we show that the secondary integral Steenrod algebra is
strictifiable.Comment: v3: Minor revision
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