Riccardo Capovilla | Centro de Investigacion y Estudios Avanzados del IPN (original) (raw)

Papers by Riccardo Capovilla

Publication View. 4785548. The self-dual spin-connection as the fundamental gravitational variabl... more Publication View. 4785548. The self-dual spin-connection as the fundamental gravitational variable /--by Riccardo Capovilla. (1991). Capovilla, Riccardo.,; University Of Maryland At College Park.--Dept. Of Physics. Abstract. Thesis research directed by Dept. of Physics.. ...

Classical and Quantum Gravity, 1992

We present a manifestly gauge covariant description of fluctuations of a relativistic extended ob... more We present a manifestly gauge covariant description of fluctuations of a relativistic extended object described by the Dirac-Nambu-Goto action with Dirac-Nambu-Goto loaded edges about a given classical solution. Whereas physical fluctuations of the bulk lie normal to its worldsheet, those on the edge possess an additional component directed into the bulk. These fluctuations couple in a non-trivial way involving the underlying geometrical structures associated with the worldsheet of the object and of its edge. We illustrate the formalism using as an example a string with massive point particles attached to its ends.

We develop the Ostrogradsky-Hamilton formalism for geodetic brane gravity, described by the Regge... more We develop the Ostrogradsky-Hamilton formalism for geodetic brane gravity, described by the Regge-Teitelboim geometric model in higher codimension. We treat this gravity theory as a second-order derivative theory, based on the extrinsic geometric structure of the model. As opposed to previous treatments of geodetic brane gravity, our Lagrangian is linearly dependent on second-order time derivatives of the field variables, the embedding functions. The difference resides in a boundary term in the action, usually discarded. Certainly, this suggests applying an appropriate Ostrogradsky-Hamiltonian approach to this type of theories. The price to pay for this choice is the appearance of second class constraints. We determine the full set of phase space constraints, as well as the gauge transformations they generate in the reduced phase space. Additionally, we compute the algebra of constraints and explain its physical content. In the same spirit, we deduce the counting of the physical deg...

Revista Mexicana De Fisica, 2000

... Charnilpa, 62250 Cuernavacn, Morelos, Mexico Janef Jemal Guven 5-y Instituto de Ciencias Nucl... more ... Charnilpa, 62250 Cuernavacn, Morelos, Mexico Janef Jemal Guven 5-y Instituto de Ciencias Nucleares, Universidad Nacional Autdnoma de MJxico Apartado postal 70-543, 04510 Mkxico, DE, Mexico ... For simplicity, we restrict our attention to Dinc-Nambu-Goto extended objects ...

In the derivation of a pure spin connection action functional for gravity two methods have been p... more In the derivation of a pure spin connection action functional for gravity two methods have been proposed. The first starts from a first order lagrangian formulation, the second from a hamiltonian formulation. In this note we show that they lead to identical results. PACS: 04.20.Cv, 04.20.Fy, 02.40.+m As shown by Ashtekar, there is a hamiltonian formulation of general relativity which uses the (spatial) self-dual spin connection as the configuration space variable.[1] The 3-metric is essentially the conjugate momentum, and therefore loses some of its priviledged status in the theory. It is possible to go one step further, and give a covariant lagrangian formulation of general relativity which employs only the (space-time) self-dual spin connection and a scalar density as the gravitational variables.[2, 3] In this “pure spin connection formulation”, the spacetime metric is merely a derived quantity, and general relativity appears as a generally covariant gauge theory of an SL(2,C) con...

Journal of Physics Communications

A simultaneous variational principle is introduced that offers a novel avenue to the description ... more A simultaneous variational principle is introduced that offers a novel avenue to the description of the equilibrium configurations, and at the same time of the elementary excitations, or undulations, of fluid lipid membranes, described by a geometric continuum free energy. The simultaneous free energy depends on the shape functions through the membrane stress tensor, and on an additional deformation spatial vector. Extremization of this free energy produces at once the Euler-Lagrange equations and the Jacobi equations, that describe elementary excitations, for the geometric free energy. As an added benefit, the energy of the elementary excitations, given by the second variation of the geometric free energy, is obtained without second variations. Although applied to the specific case of lipid membranes, this variational principle should be useful in any physical system where bending modes are dominant. The wide range of validity exhibited by variational principles in theoretical physics makes them either the ultimate fundamental tool in the understanding of physical phenomena, or a sort of mathematical indulging by the theoretical physicist, depending on the point of view. In soft matter physics, the prevailing attitude appears to be the latter, leaning more towards Mach than Planck [1]. In order to try to reverse this tendency, this note introduces a simultaneous variational principle for the unified description of the equilibrium configurations, and of the elementary excitations, or small perturbations about equilibrium, of lipid membranes. Lipid membranes provide a paradigmatic example of a two-dimensional soft material, where bending deformations are dominant [2]. As a research subject, lipid membranes sit at the crossroad of soft matter physics, biophysics, material science, and field theory [3-6]. There is also a close formal relationship to relativistic field theory, and the whole theory of relativistic extended objects, or branes, especially when considered as effective models, for example of black hole horizons [7], of topological defects in cosmology [8], or of hadrons in QCD [9]. The common theme is an effective description of physical systems in terms of geometrical continuum degrees of freedom, and the symmetry of reparametrization invariance, that for relativistic models is due to the underlying symmetry of the background spacetime, for membranes is due to their fluid state, or negligibile shear. The main advantage that lipid membranes possess with respect to other physical systems, real or possible, is the enormous wealth of experimental data, both available and accessible, that provides an exciting and welcome guidance to the theoretician's fecund imagination. For this reason, it is sensible to use the physics of lipid membranes as a paradigm for the study of the elementary bending excitations of a great variety of physical systems. At mesoscopic scales, an homogenous fluid lipid membrane can be considered as an infinitely thin surface, described by an effective geometric, reparametrization invariant, free energy. Effective curvature geometric models, and in particular the classic Canham-Helfrich free energy [10-12], provide a remarkably reliable description of the configurations and of the mechanical response of physical lipid membranes [13-15]. The curvature model is defined by a reparametrization invariant free energy built with geometric scalar in terms of the intrinsic and extrinsic geometries of the surface that represents the membrane, or equivalently in terms of covariant derivatives of the shape functions, given by the surface integral of the energy density

Class Quantum Gravity, 1990

Avance Y Perspectiva, 2005

Phys Rev D, 1994

We show that the quantum super-minisuperspace of N=1 supergravity with Λ = 0 has no non-trivial p... more We show that the quantum super-minisuperspace of N=1 supergravity with Λ = 0 has no non-trivial physical states for class A Bianchi models. Hence, in super quantum cosmology, the vanishing of Λ is a condition for the existence of the universe. We argue that this result implies that in full supergravity with Λ there are no non-trivial physical states with a finite number of fermionic fields. We use the Jacobson canonical formulation.

The form of the initial value constraints in Ashtekar's hamiltonian formulation of general re... more The form of the initial value constraints in Ashtekar's hamiltonian formulation of general relativity is recalled, and the problem of solving them is compared with that in the traditional metric variables. It is shown how the general solution of the four diffeomorphism constraints can be obtained algebraically provided the curvature is non-degenerate, and the form of the remaining (Gauss law)

Lettere al Nuovo Cimento Series 2, 1985

We present a simple five-dimensional cosmological model in which a static behaviour of the compac... more We present a simple five-dimensional cosmological model in which a static behaviour of the compactified dimension is allowed, leading to static gauge and gravitational coupling constants.

Physical Review E, 2002

Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadra... more Consider a lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature of its geometry; that describing the edge is proportional to its length. In this note we determine the boundary conditions satisfied by the equilibria of the membrane on this edge, exploiting variational principles. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to earlier work for axially symmetric configurations, we discover the existence of an additional boundary condition which is identically satisfied in that limit. By considering the balance of the forces operating at the edge, we provide a physical interpretation for the boundary conditions. We end with a discussion of the effect of the addition of a Gaussian rigidity term for the membrane.

Nuclear Physics B - Proceedings Supplements, 1997

Abstract We consider, from a geometrical point of view, the dynamics of a relativistic extended o... more Abstract We consider, from a geometrical point of view, the dynamics of a relativistic extended object with loaded edges, and of extended objects joined at some interface. We focus on the case of a Dirac-Nambu-Goto [DNG] object with DNG edges.

Journal of Physics: Condensed Matter, 2004

We consider lipid fluid vesicles described by the Helfrich Hamiltonian. We develop a geometricall... more We consider lipid fluid vesicles described by the Helfrich Hamiltonian. We develop a geometrically covariant approach to derive the appropriate equilibrium conditions for these objects. This also allows us to derive general expressions for the stresses and torques acting within the vesicle. The appropriate generalization to models for inhomogeneous lipid vesicles is briefly described.

ABSTRACT We review our recent work on the covariant treatment of the kinematics of infinitesimal ... more ABSTRACT We review our recent work on the covariant treatment of the kinematics of infinitesimal deformations of the worldsheet spanned in spacetime by a relativistic membrane. We also describe a coupled system of non-linear partial differential equations which describes non-perturbatively the evolution of large deformations of an extremal relativistic membrane. These can be seen as higher-dimensional analogs of the Raychaudhuri equations for point particles.

Journal of Geometry and Symmetry in Physics

Geometric continuum models for fluid lipid membranes are considered using classical field theory,... more Geometric continuum models for fluid lipid membranes are considered using classical field theory, within a covariant variational approach. The approach is cast as a higher-derivative Lagrangian formulation of continuum classical field theory, and it can be seen as a covariant version of the field theoretical variational approach that uses the height representation. This novel Lagrangian formulation is presented first for a generic reparametrization invariant geometric model, deriving its equilibrium condition equation, or shape equation, and its linear and angular stress tensors, using the classical Canham-Helfrich elastic bending energy for illustration. The robustness of the formulation is established by extending it to the presence of external forces, and to the case of heterogenous lipid membranes, breaking reparametrization invariance. In addition, a useful and compact general expression for the second variation of the free energy is obtained within the Lagrangian formulation, as a first step towards the study of the stability of membrane configurations. The simple structure of the expressions derived for the basic entities that appear in the mechanics of a lipid membrane is a direct consequence of the well established power of a Lagrangian variational approach. The paper is self-contained, and it is meant to provide, besides a new framework, also a convenient introduction to the mechanics of lipid membranes.

Annals of Physics

A covariant simultaneous action for branes in an arbitrary curved background spacetime is conside... more A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In this note, we consider geometric models depending only on the intrinsic geometry of the brane worldvolume, and discuss briefly the generalization to extrinsic geometry dependent models. The approach is illustrated for Dirac-Nambu-Goto [DNG] branes. For a relativistic particle, a simultaneous action was introduced by Bażański, that served as an inspiration for the present work.