The Algebra of the Energy-Momentum Tensor and the Noether Currents in Classical Non-Linear Sigma Models

The recently derived current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor $\theta_{\mu\nu}$, the Noether current $j_\mu$ associated with the global symmetry of the theory and the composite field $j$ appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of $j_\mu$ and $j$, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge $\, c\!=\!0$, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody / Sugawara type construction.Comment: 10 pages, THEP 92/2

Current Algebra of Classical Non-Linear Sigma Models

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current $j_\mu$ associated with the global symmetry of the theory, a composite scalar field $j$, the algebra closes under Poisson brackets.Comment: 6 page

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory

We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.Comment: 50 page

The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic manifolds. It is well defined for a certain class of differential forms that we propose to call Poisson forms and turns the space of Poisson forms into a Lie superalgebra.Comment: 40 pages LaTe

Effects of blocking developmental cell death on sexually dimorphic calbindin cell groups in the preoptic area and bed nucleus of the stria terminalis

Background: Calbindin-D28 has been used as a marker for the sexually dimorphic nucleus of the preoptic area (SDN-POA). Males have a distinct cluster of calbindin-immunoreactive (ir) cells in the medial preoptic area (CALB-SDN) that is reduced or absent in females. However, it is not clear whether the sex difference is due to the absolute number of calbindin-ir cells or to cell position (that is, spread), and the cellular mechanisms underlying the sex difference are not known. We examined the number of cells in the CALB-SDN and surrounding regions of C57Bl/6 mice and used mice lacking the pro-death gene, Bax, to test the hypothesis that observed sex differences are due to cell death. Methods: Experiment 1 compared the number of cells in the CALB-SDN and surrounding regions in adult males, females, and females injected with estradiol benzoate on the day of birth. In experiment 2, cell number in the CALB-SDN and adjacent regions were compared in wild-type and Bax knockout mice of both sexes. In addition, calbindin-ir cells were quantified within the principal nucleus of the bed nucleus of the stria terminalis (BNSTp), a nearby region that is larger in males due to Bax-dependent cell death. Results: Males had more cells in the CALB-SDN as well as in surrounding regions than did females, and estradiol treatment of females at birth masculinized both measures. Bax deletion had no effect on cell number in the CALB-SDN or surrounding regions but increased calbindin-ir cell number in the BNSTp. Conclusions: The sex difference in the CALB-SDN of mice results from an estrogen-dependent difference in cell number with no evidence found for greater spread of cells in females. Blocking Bax-dependent cell death does not prevent sex differences in calbindin-ir cell number in the BNST or CALB-SDN but increases calbindin-ir cell number in the BNSTp of both sexes

Currents, Charges, and Canonical Structure of Pseudodual Chiral Models

We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the symmetries of the usual chiral model. We refine the conventional algorithm to more efficiently produce the nonlocal symmetries of the model, and we discuss the complete local current algebra for the pseudodual theory. We also exhibit the canonical transformation which connects the usual chiral model to its fully equivalent dual, further distinguishing the pseudodual theory.Comment: 15 pages, ANL-HEP-PR-93-85,Miami-TH-1-93,Revtex (references updated, format improved to Revtex