1,034 research outputs found
Products, coproducts and singular value decomposition
Products and coproducts may be recognized as morphisms in a monoidal tensor
category of vector spaces. To gain invariant data of these morphisms, we can
use singular value decomposition which attaches singular values, ie generalized
eigenvalues, to these maps. We show, for the case of Grassmann and Clifford
products, that twist maps significantly alter these data reducing degeneracies.
Since non group like coproducts give rise to non classical behavior of the
algebra of functions, ie make them noncommutative, we hope to be able to learn
more about such geometries. Remarkably the coproduct for positive singular
values of eigenvectors in yields directly corresponding eigenvectors in
A\otimes A.Comment: 17 pages, three eps-figure
A Hopf laboratory for symmetric functions
An analysis of symmetric function theory is given from the perspective of the
underlying Hopf and bi-algebraic structures. These are presented explicitly in
terms of standard symmetric function operations. Particular attention is
focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and
twisted products (Rota cliffordizations) induced by branching operators in the
symmetric function context. The latter are shown to include the algebras of
symmetric functions of orthogonal and symplectic type. A commentary on related
issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat
On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form
Clifford algebras are naturally associated with quadratic forms. These
algebras are Z_2-graded by construction. However, only a Z_n-gradation induced
by a choice of a basis, or even better, by a Chevalley vector space isomorphism
Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition
into scalars, vectors, tensors, and so on, mandatory in physics. We show that
the Chevalley isomorphism theorem cannot be generalized to algebras if the
Z_n-grading or other structures are added, e.g., a linear form. We work with
pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which
we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford
algebras'. It turns out, that in this sense, all multi-vector Clifford algebras
of the same quadratic but different bilinear forms are non-isomorphic. The
usefulness of such algebras in quantum field theory and superconductivity was
shown elsewhere. Allowing for arbitrary bilinear forms however spoils their
diagonalizability which has a considerable effect on the tensor decomposition
of the Clifford algebras governed by the periodicity theorems, including the
Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which
can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1}
\otimes Cl_{1,1}. The general case used in quantum field theory lacks this
feature. Theories with non-symmetric bilinear forms are however needed in the
analysis of multi-particle states in interacting theories. A connection to
q-deformed structures through nontrivial vacuum states in quantum theories is
outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International
Conference on Clifford Algebras and their Applications in Mathematical
Physics, Ixtapa, Mexico, June 27 - July 4, 199
Management of infertility in a patient presenting with ovarian dysfunction and McCune-Albright syndrome
Persistent autonomous ovarian dysfunction in McCune-Albright syndrome
(MAS) patients is associated with the development of multiple dominant
follicles, premature luteinization, cyst formation, and anovulatory
infertility. Due to the mosaic distribution of the mutation, ovaries may
be unequally affected. In the current patient, the least affected ovary
became quiescent upon GnRH agonist-induced gonadotropin suppression.
Normoovulatory cycles were restored after subsequent removal of the
affected right ovary, and a pregnancy was established within 3 months. A
healthy unaffected girl was born at term after an uneventful pregnancy.
The placental tissue was normal, and the mutation was not detected in the
placenta, umbilical cord structures, or umbilical cord blood. GnRH analog
administration may help to identify those MAS patients who might benefit
from unilateral ovariectomy. Because a healthy baby was born, evidence is
provided suggesting that MAS is not passed on to the children from the
parents
Quantum field theory and Hopf algebra cohomology
We exhibit a Hopf superalgebra structure of the algebra of field operators of
quantum field theory (QFT) with the normal product. Based on this we construct
the operator product and the time-ordered product as a twist deformation in the
sense of Drinfeld. Our approach yields formulas for (perturbative) products and
expectation values that allow for a significant enhancement in computational
efficiency as compared to traditional methods. Employing Hopf algebra
cohomology sheds new light on the structure of QFT and allows the extension to
interacting (not necessarily perturbative) QFT. We give a reconstruction
theorem for time-ordered products in the spirit of Streater and Wightman and
recover the distinction between free and interacting theory from a property of
the underlying cocycle. We also demonstrate how non-trivial vacua are described
in our approach solving a problem in quantum chemistry.Comment: 39 pages, no figures, LaTeX + AMS macros; title changed, minor
corrections, references update
Nonsupplemented luteal phase characteristics after the administration of recombinant human chorionic gonadotropin, recombinant luteinizing hormone, or gonadotropin-releasing hormone (GnRH) agonist to induce final oocyte maturation in in vitro fertilization patients after ovarian stimulation with recombinant follicle-stimulating hormone and GnRH antagonist cotreatment
Replacing GnRH agonist cotreatment for the prevention of a premature rise
in LH during ovarian stimulation for in vitro fertilization (IVF) by the
late follicular phase administration of GnRH antagonist may render
supplementation of the luteal phase redundant, because of the known rapid
recovery of pituitary function after antagonist cessation. This randomized
two-center study was performed to compare nonsupplemented luteal phase
characteristics after three different strategies for inducing final oocyte
maturation. Forty patients underwent ovarian stimulation using recombinant
(r-)FSH (150 IU/d, fixed) combined with a GnRH antagonist (antide; 1 mg/d)
during the late follicular phase. When at least one follicle above 18 mm
was observed, patients were randomized to induce oocyte maturation by a
single injection of either r-human (h)CG (250 microg) (n = 11), r-LH (1
mg) (n = 13), or GnRH agonist (triptorelin; 0.2 mg) (n = 15). Retrieved
oocytes were fertilized by either IVF or intracytoplasmatic sperm
injection, depending on sperm quality. Embryo transfer was performed 3-4 d
after oocyte retrieval. No luteal support was provided. Serum
concentrations of FSH, LH, estradiol (E(2)), progesterone (P), and hCG
were assessed at fixed intervals during the follicular and luteal phase.
The median duration of the luteal phase was 13, 10, and 9 d for the r-hCG,
the r-LH, and the GnRH agonist group, respectively (P = 0.005). The median
area under the curve per day (from 4 d post randomization until the onset
of menses) for LH was 0.50, 2.34, and 1.07 for the r-hCG, the r-LH, and
the GnRH agonist group, respectively (P = 0.001). The median area under
the curve per day for P was 269 vs. 41 and 16 for the r-hCG, the r-LH, and
the GnRH agonist group, respectively (P < 0.001). Low pregnancy rates
(overall, 7.5%; range, 0-18% per started cycle) were observed in all
groups. In conclusion, the nonsupplemented luteal phase was insufficient
in all three groups. In the patients receiving r-hCG, the luteal phase was
less disturbed, compared with both other groups, presumably because of
prolonged clearance of hCG from the circulation and the resulting extended
support of the corpus luteum. Despite high P and E(2) concentrations
during the early luteal phase in all three groups, luteolysis started
prematurely, presumably because of excessive negative steroid feedback
resulting in suppressed pituitary LH release. Hence, support of corpus
luteum function remains mandatory after ovarian stimulation for IVF with
GnRH antagonist cotreatment
The structure of Green functions in quantum field theory with a general state
In quantum field theory, the Green function is usually calculated as the
expectation value of the time-ordered product of fields over the vacuum. In
some cases, especially in degenerate systems, expectation values over general
states are required. The corresponding Green functions are essentially more
complex than in the vacuum, because they cannot be written in terms of standard
Feynman diagrams. Here, a method is proposed to determine the structure of
these Green functions and to derive nonperturbative equations for them. The
main idea is to transform the cumulants describing correlations into
interaction terms.Comment: 13 pages, 6 figure
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