We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero-modes should be handled in order to avoid overcounting of degrees of freedom. This is an issue that has been overlooked in many recent contributions on the derivation of domain wall effective actions. We show that, unless such redundancy is completely removed by means of a sort of gauge fixing, the expression obtained for the effective action will not be consistent. We readdress some earlier calculations over the existence of curvature corrections in the light of the previous discussion and briefly comment on the application of this method to higher dimensional topological defects.

We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic curvature of its worldline, {\ie} $S=\alpha\int ds \kappa$. This geometrical particle system possesses one extra gauge invariance besides reparametrizations, and the full gauge algebra has been previously identified as classical $\W_3$. The key observation is that the covariantly reduced phase space of this model can be naturally identified with the spinor and twistor descriptions of the covariant phase spaces associated with massless particles of helicity $s=\alpha$. Then, standard quantization techniques require $\alpha$ to be quantized and show how the associated Hilbert spaces are solution spaces of the standard relativistic massless wave equations with $s=\alpha$. Therefore, providing us with a simple particle model for Weyl fermions ($\alpha=1/2$), Maxwell fields ($\alpha=1$), and higher spin fields. Moreover, one can go a little further and in the Maxwell case show that, after a suitable redefinition of constraints, the standard Dirac quantization procedure for first-class constraints leads to a wave-function which can be identified with the gauge potential $A_\mu$. Gauge symmetry appears in the formalism as a consequence of the invariance under $\W_3$-morphisms, that is, exclusively in terms of the extrinsic geometry of paths in Minkowski space. When all gauge freedom is fixed one naturally obtains the standard Lorenz gauge condition on $A_{\mu}$, and Maxwell equations in that gauge. This construction has a direct generalization to arbitrary integer values of $\alpha$, and we comment on the physically interesting case of linearized Einstein gravity ($\alpha =2$).

We provide a description of W3 transformations in terms of deformations of convex curves in two dimensional Euclidean space. This geometrical interpretation sheds some light on the nature of finite W3-morphisms. We also comment on how this construction can be extended to the case of Wn and “nicely curved” curves in Rn−1.

In a previous study we tried to assess the clinical usefulness of platelet count (PIC) to confirm whether postoperative pulmonary embolism could be suspected early. Unexpectedly, the 19 patients who subsequently developed pulmonary embolism had significantly lower mean PIC levels even before surgery. In an attempt to discover whether the preoperative PIC levels were associated with a different incidence of postoperative blood loss, we decided to retrospectively study the relationship between preoperative PIC levels and the consequences of blood loss. There were 459 consecutive patients undergoing hip surgery. After excluding 5 patients who died during the first 3 postoperative days, and 16 patients who bled from a definitive anatomic site, there were 438 patients. Blood loss was considered to be excessive when two or more of the following conditions were present: (1) total transfusion requirements exceeding 1,000 ml whole blood or 2 units of packed red cells; (2) a drop in hemoglobin level of 5 g/dl or more, and (3) a hemoglobin level below 8 g/dl at any moment during the first 8 postoperative days. Blood loss was considered to be excessive in 91 patients. Preoperative PIC levels were significantly lower in these patients as compared to patients without the condition (204 ± 52 vs. 236 ± 79 × 109 liter–1; p = 0.0002). When patients were classified according to the quartiles of preoperative PIC, the odds ratio of developing excessive blood loss was 0.69 (95% CI: 0.38-1.26) in patients in the second quartile; 0.57 (95% CI: 0.30-1.06) in the third quartile, and 0.27 (95% CI: 0.13-0.57) in patients in the highest quartile. After adjusting for age, sex, type of surgery and type of prophylaxis, the preoperative PIC levels maintained a statistically significant inverse correlation with postoperative blood loss.

We show that W_3 is the algebra of symmetries of the ``rigid-particle'', whose action is given by the integrated extrinsic curvature of its world line. This is easily achived by showing that its equation of motion can be written in terms of the Boussinesq operator. We also show how to obtain the equations of motion of the standard relativistic particle provided it is consistent to impose the ``zero-curvature gauge'', and comment about its connection with the KdV operator.

We prove that W-3 is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in terms of the Boussinesq operator. The W-3 generators T and W then appear respectively as functions of the induced world line metric and the extrinsic curvature. We also show how the equations of motion for the standard relativistic particle arise from those of the rigid particle whenever it is consistent to impose the ''zero-curvature gauge'', and how to rewrite them in terms of the KdV operator. The relation between particle models and integrable systems is further pursued in the case of the spinning particle, whose equations of motion are closely related to the SKdV operator. We also partially extend our analysis in the supersymmetric domain to the scale-invariant rigid particle by explicitly constructing a supercovariant version of its action.

We prove that particle models whose action is given by the integrated nth curvature function over the world line possess n + 1 gauge invariances. A geometrical characterization of these symmetries is obtained via Frenet equations by rephrasing the nth curvature model in Rd in terms of a standard relativistic particle in Sd-n. We “prove by example” that the algebra of these infinitesimal gauge invariances is nothing but Wn+2, thus providing a geometrical picture of the W-symmetry for these models. As a spin-off of our approach we give a new global invariant for four-dimensional curves subject to a curvature constraint.

We introduce a particle mechanics model with Sp(2M) gauge invariance. Different partial gauge-fixings by means of sl(2) embeddings on the gauge algebra lead to reduced models which are invariant under diffeomorphisms and classical non-linear W-transformations as the residual gauge symmetries thus providing a set of models of gauge and matter fields coupled in a W-invariant way. The equations of motion for the matter variables give Lax operators in a matrix form. We examine several examples in detail and discuss the issue of integration of infinitesimal W-transformations.

Classical W-3 transformations are discussed as restricted diffeomorphism transformations (W-Diff) in two-dimensional space. We formulate them by using Riemannian geometry as a basic ingredient. The extended W-3 generators are given as particular combinations of Christoffel symbols. The defining equations of W-Diff are shown to depend on these generators explicitly. We also consider the issues of finite transformations, global SL(3) transformations and W-Schwarzians.

We propose a set of Sp(2M) gauge invariant particle mechanical models. By applying the classical Drinfeld-Sokolov reduction mechanism, non-linear W-symmetries are shown to appear as the residual gauge transformations.

A free-field formulation of N=2 topological supergravity is obtained with a suitable gauge fixing of two-dimensional topological Yang-Mills theory, taking as the gauge group a contraction of Osp(2|2). We also give a superfield description of the action and its symmetry currents.

The quantization of a higher-order derivative Lagrangian for a relativistic spinning particle is performed. The Dirac equation is recovered.

We consider the open and closed gauge algebras for the spinning particle resulting from two different sets of gauge generators. Using the Batalin-Vilkovisky lagrangian formalism, the BRST and anti-BRST generators are constructed for both cases.

Using the field-antifield formalism and the Dirac constraint analysis we present, in a gauge independent way, the lagrangian and hamiltonian BRST structures of the spinning string.

We show the existence of a generalized anti-BRST symmetry in the space of fields and antifields. The gauge-fixed symmetry and its nilpotency are studied. Explicit expressions for irreducible and off-shell reducible theories with a closed gauge algebra are given.

Introducing the BRST symmetry in the space of fields and antifields a BRST charge at the lagrangian level is constructed in a gauge invariant way. For the case of irreducible first rank theories, we establish, at the classical level, the equivalence of the field-antifield formalism with the standard BRST formalism.

We establish, at the classical level, the equivalence between the standard BRST hamiltonian formalism and the lagranian BRST approach with fields and antifields for irreducible first rank theories.

The BRST-invariant path integral formalism is used in order to calculate the propagator for spinless and spinning non-relativistic particles.

The authors compute the propagator of a free spinless relativistic particle in a generic relativistic gauge d lambda d tau =f( lambda ). A criterion is given to decide whether a particular gauge fixing is valid or not.