130 research outputs found
The sh Lie structure of Poisson brackets in field theory
A general construction of an sh Lie algebra from a homological resolution of
a Lie algebra is given. It is applied to the space of local functionals
equipped with a Poisson bracket, induced by a bracket for local functions along
the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order
maps are constructed which combine to form an sh Lie algebra on the graded
differential algebra of horizontal forms. The same construction applies for
graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket
of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.Comment: 24 pages Latex fil
Courant sigma model and -algebras
The Courant sigma model is a 3-dimensional topological sigma model of AKSZ
type which has been used for the systematic description of closed strings in
non-geometric flux backgrounds. In particular, the expression for the fluxes
and their Bianchi identities coincide with the local form of the axioms of a
Courant algebroid. On the other hand, the axioms of a Courant algebroid also
coincide with the conditions for gauge invariance of the Courant sigma model.
In this paper we embed this interplay between background fluxes of closed
strings, gauge (or more precisely BRST) symmetries of the Courant sigma model
and axioms of a Courant algebroid into an -algebra structure. We show
how the complete BV-BRST formulation of the Courant sigma model is described in
terms of -algebras. Moreover, the morphism between the
-algebra for a Courant algebroid and the one for the corresponding
sigma model is constructed.Comment: 34 pages. v2: typos corrected, published versio
Algebra Structures on Hom(C,L)
We consider the space of linear maps from a coassociative coalgebra C into a
Lie algebra L. Unless C has a cocommutative coproduct, the usual symmetry
properties of the induced bracket on Hom(C,L) fail to hold. We define the
concept of twisted domain (TD) algebras in order to recover the symmetries and
also construct a modified Chevalley-Eilenberg complex in order to define the
cohomology of such algebras
Noether's second theorem for BRST symmetries
We present Noether's second theorem for graded Lagrangian systems of even and
odd variables on an arbitrary body manifold X in a general case of BRST
symmetries depending on derivatives of dynamic variables and ghosts of any
finite order. As a preliminary step, Noether's second theorem for Lagrangian
systems on fiber bundles over X possessing gauge symmetries depending on
derivatives of dynamic variables and parameters of arbitrary order is proved.Comment: 31 pages, to be published in J. Math. Phy
Classical field theory. Advanced mathematical formulation
In contrast with QFT, classical field theory can be formulated in strict
mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second
Noether theorems provide BRST extension of this classical field theory by means
of ghosts and antifields for the purpose of its quantization.Comment: 30 p
Noether's second theorem in a general setting. Reducible gauge theories
We prove Noether's direct and inverse second theorems for Lagrangian systems
on fiber bundles in the case of gauge symmetries depending on derivatives of
dynamic variables of an arbitrary order. The appropriate notions of reducible
gauge symmetries and Noether's identities are formulated, and their equivalence
by means of certain intertwining operator is proved.Comment: 20 pages, to be published in J. Phys. A (2005
The KT-BRST complex of a degenerate Lagrangian system
Quantization of a Lagrangian field system essentially depends on its
degeneracy and implies its BRST extension defined by sets of non-trivial
Noether and higher-stage Noether identities. However, one meets a problem how
to select trivial and non-trivial higher-stage Noether identities. We show
that, under certain conditions, one can associate to a degenerate Lagrangian L
the KT-BRST complex of fields, antifields and ghosts whose boundary and
coboundary operators provide all non-trivial Noether identities and gauge
symmetries of L. In this case, L can be extended to a proper solution of the
master equation.Comment: 15 pages, accepted for publication in Lett. Math. Phy
Lymphatic vasculature mediates macrophage reverse cholesterol transport in mice
Reverse cholesterol transport (RCT) refers to the mobilization of cholesterol on HDL particles (HDL-C) from extravascular tissues to plasma, ultimately for fecal excretion. Little is known about how HDL-C leaves peripheral tissues to reach plasma. We first used 2 models of disrupted lymphatic drainage from skin — 1 surgical and the other genetic — to quantitatively track RCT following injection of [3H]-cholesterol–loaded macrophages upstream of blocked or absent lymphatic vessels. Macrophage RCT was markedly impaired in both models, even at sites with a leaky vasculature. Inhibited RCT was downstream of cholesterol efflux from macrophages, since macrophage efflux of a fluorescent cholesterol analog (BODIPY-cholesterol) was not altered by impaired lymphatic drainage. We next addressed whether RCT was mediated by lymphatic vessels from the aortic wall by loading the aortae of donor atherosclerotic Apoe-deficient mice with [2H]6-labeled cholesterol and surgically transplanting these aortae into recipient Apoe-deficient mice that were treated with anti-VEGFR3 antibody to block lymphatic regrowth or with control antibody to allow such regrowth. [2H]-Cholesterol was retained in aortae of anti–VEGFR3-treated mice. Thus, the lymphatic vessel route is critical for RCT from multiple tissues, including the aortic wall. These results suggest that supporting lymphatic transport function may facilitate cholesterol clearance in therapies aimed at reversing atherosclerosis
Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras
The algebraic and geometric structures of deformations are analyzed
concerning topological field theories of Schwarz type by means of the
Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in
three dimensions induces the Courant algebroid structure on the target space as
a sigma model. Deformations of BF theories in dimensions are also analyzed.
Two dimensional deformed BF theory induces the Poisson structure and three
dimensional deformed BF theory induces the Courant algebroid structure on the
target space as a sigma model. The deformations of BF theories in
dimensions induce the structures of Batalin-Vilkovisky algebras on the target
space.Comment: 25 page
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