Open-closed homotopy algebra in mathematical physics

In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures ($A_\infty$-algebras) by closed strings ($L_\infty$-algebras).Comment: 38 pages, 4 figures; v2: published versio

Reducing Computational Costs in the Basic Perturbation Lemma

Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, the Basic Perturbation Lemma, presents, in general, high computational costs. In this paper, we propose a general strategy in order to reduce the complexity in some important formulas (those following a specific pattern) obtained by this algorithm. Then, we show two examples of application of this methodology.

Batalin-Vilkovisky Integrals in Finite Dimensions

The Batalin-Vilkovisky method (BV) is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges associated with symmetries that do not close off-shell. Homological Perturbation Theory is introduced and used to develop the integration theory behind BV and to describe the BV quantization of a Lagrangian system with symmetries. Localization (illustrated in terms of Duistermaat-Heckman localization) as well as anomalous symmetries are discussed in the framework of BV.Comment: 35 page

Irreducible Hamiltonian approach to the Freedman-Townsend model

The irreducible BRST symmetry for the Freedman-Townsend model is derived. The comparison with the standard reducible approach is also addressed.Comment: 18 pages, LaTeX 2.0

Irreducible Hamiltonian BRST approach to topologically coupled abelian forms

An irreducible Hamiltonian BRST approach to topologically coupled p- and (p+1)-forms is developed. The irreducible setting is enforced by means of constructing an irreducible Hamiltonian first-class model that is equivalent from the BRST point of view to the original redundant theory. The irreducible path integral can be brought to a manifestly Lorentz covariant form.Comment: 29 pages, LaTeX 2.0

Irreducible Hamiltonian BRST symmetry for reducible first-class systems

An irreducible Hamiltonian BRST quantization method for reducible first-class systems is proposed. The general theory is illustrated on a two-stage reducible model, the link with the standard reducible BRST treatment being also emphasized.Comment: Latex 2.09, 23 pages, to appear in Int. J. Mod. Phys.

A Note on "Irreducible" p-Form Gauge Theories with Stueckelberg Coupling

p-form gauge theories with Stueckelberg coupling are quantized in an irreducible antifield-BRST way. As a consequence, neither the ghosts of ghosts nor their antifields appear. Some irreducible gauge conditions are inferred naturally within our formalism. In the end we briefly discuss the interacting case.Comment: 10 pag, latex 2.09, no figure

Primary versus delayed repair for bile duct injuries sustained during cholecystectomy: results of a survey of the Association Francaise de Chirurgie

BACKGROUND: Bile duct injuries (BDIs) sustained during a cholecystectomy still remain a major surgical problem, and it is still not clear whether the injury should be repaired immediately or a delayed repair is preferred. METHODS: A retrospective national French survey was conducted to compare the results of immediate (at time of cholecystectomy), early (within 45 days after a cholecystectomy) and late (beyond 45 days after a cholecystectomy) surgical repair for BDI sustained during a cholecystectomy. RESULTS: Forty-seven surgical centres provided 640 cases of bile duct injury sustained during a cholecystectomy of which 543 were analysed for the purpose of the present study. The timing of repair was immediate in 194 cases (35.7%), early in 216 cases (39.8%) and late in 133 cases (24.5%). The type of repair was a suture repair in 157 cases (81%), and a bilio-digestive reconstruction in 37 cases (19%) for immediate repair; a suture repair in 119 cases (55.1%) and a bilio-digestive anastomosis in 96 cases (44.9%) for the early repair; and a bilio-digestive reconstruction in 129 cases (97%) and a suture repair in 4 cases (3%) for late repair. A second procedure was required in 110 cases (56.7%) for immediate repair, 80 cases (40.7%) for early repair (P < 0.05) and in 9 cases (6.8%) for late repair (P < 0.001). CONCLUSION: The timing of surgical repair for a bile duct injury sustained during a cholecystectomy influences significantly the rate of a second procedure and a late repair should be preferred option

Irreducible antifield-BRST approach to reducible gauge theories

An irreducible antifield BRST quantization method for reducible gauge theories is proposed. The general formalism is illustrated in the case of the Freedman-Townsend model.Comment: 19 pages, LaTeX 2.0

Invariants from classical field theory

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S^3, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.Comment: 20 pages, 1 figure, to appear in J. Math. Phy