A theory of generally invariant lagrangians for the metric fields. II

The second-order generally invariant Lagrangians for the metric fields on anyn-dimensional manifold are studied as certain special coordinate functions on a space of jets. The number of independent Lagrangians of this type is determined. The dimensionsn=3 andn=4 are examined in detail with the help of a computer.     

A class of exact solutions for coupled electromagnetic and scalar fields for einstein-rosen metric. I

A class of rigorous solutions for the Einstein-Rosen nonstatic cylindrically symmetric metric in the presence of combined electromagnetic and scalar meson fields has been obtained. Some of these solutions reduce to the solutions obtained by Misra and Radhakrishna [Proc. Nat. Inst. Sci. India Part A 28 (1962), 632] when the scalar field is not present.     

Tetrad fields and metric tensor in the gauge theory of gravitation

The most relevant geometrical aspects of the gauge theory of gravitation are considered. A global definition of the tetrad fields is given and emphasis is placed on their role in defining an isomorphism between the tangent bundle of space-time and an appropriate vector bundle B associated to the gauge bundle. It is finally shown how to construct the fundamental geometrical objects on space-time, starting from B.     

Symplectic approach to the theory of quantized fields. I

Our aim in this paper the first one of a series concerned with the problem of field quantization starting from the symplectic structure underlying the classical theory, is to build up the variational theory necessary to all further constructions. The basic notions are the vertical bundle and thestructure 1-form used to define thegeneralized infinitesimal contact transformation which allows us to state and solve the variational problem related to field physics.Giving a system of modulevalued differential forms of different degree on the vertical bundle which solutions are the stationary cross sections is the main result in the paper. In this scheme the Euler-Lagrange classical equations are the expressions induced by such a system of differential forms on any cross section of the vertical bundle. This gives us a complete linearization of the Euler-Lagrange equations and, starting from it, a natural globalization of these equations. Finally, the notion of variational problem invariant by a Lie group is defined in this scheme, Noether's theorem related to such invariant problem is formulated and an intrinsic version of the so-called Noether invariants of classical variational calculus is obtained.This work has been realized in the Seminar of Mathematical Physics, directed by ProfessorJ. Sancho, in the Faculty of Science at the University of Barcelona (Spain).     

Quantization of non-abelian gauge theory. I. Gauge invariant Hamiltonian formulation

An essentially gauge invariant canonical Hamiltonian formulation is given for a non-Abelian Yang-Mills system coupled to a fermion field. The Hamiltonian contains only unconstrained dynamical variables, which in the quantum version satisfy canonical equal time commutation relations.     

Ergodic theory and visualization. I. Mesochronic plots for visualization of ergodic partition and invariant sets

We present a computational study of a visualization method for invariant sets based on ergodic partition theory, first proposed by Mezic? (Ph.D. thesis, Caltech, 1994) and Mezic? and Wiggins [Chaos 9, 213 (1999)]. The algorithms for computation of the time averages of observables on phase space are developed and used to provide an approximation of the ergodic partition of the phase space. We term the graphical representation of this approximation--based on time averages of observables--a mesochronic plot (from Greek: meso--mean, chronos--time). The method is useful for identifying low-dimensional projections (e.g., two-dimensional slices) of invariant structures in phase spaces of dimensionality bigger than two. We also introduce the concept of the ergodic quotient space, obtained by assigning a point to every ergodic set, and provide an embedding method whose graphical representation we call the mesochronic scatter plot. We use the Chirikov standard map as a well-known and dynamically rich example in order to illustrate the implementation of our methods. In addition, we expose applications to other higher dimensional maps such as the Froe?schle map for which we utilize our methods to analyze merging of resonances and, the three-dimensional extended standard map for which we study the conjecture on its ergodicity [I. Mezic?, Physica D 154, 51 (2001)]. We extend the study in our next paper [Z. Levnajic? and I. Mezic?, e-print arXiv:0808.2182] by investigating the visualization of periodic sets using harmonic time averages. Both of these methods are related to eigenspace structure of the Koopman operator [I. Mezic? and A. Banaszuk, Physica D 197, 101 (2004)].     

Gauge invariant and gauge fixed actions for various higher-spin fields from string field theory

We propose a systematic procedure for extracting gauge invariant and gauge fixed actions for various higher-spin gauge field theories from covariant bosonic open string field theory. By identifying minimal gauge invariant part for the original free string field theory action, we explicitly construct a class of covariantly gauge fixed actions with BRST and anti-BRST invariance. By expanding the actions with respect to the level N   of string states, the actions for various massive fields including higher-spin fields are systematically obtained. As illustrating examples, we explicitly investigate the level N?3$N?3$ part and obtain the consistent actions for massive graviton field, massive 3rd rank symmetric tensor field, or anti-symmetric field. We also investigate the tensionless limit of the actions and explicitly derive the gauge invariant and gauge fixed actions for general rank n symmetric and anti-symmetric tensor fields.     

A set of invariant quality factors measuring the deviation from the Kerr metric

A number of scalar invariant characterizations of the Kerr solution are presented. These characterizations come in the form of quality factors defined in stationary space-times. A quality factor is a scalar quantity varying in the interval $[0,1]$ with the value 1 being attained if and only if the space-time is locally isometric to the Kerr solution. No knowledge of the Kerr solution is required to compute these quality factors. A number of different possibilities arise depending on whether the space-time is Ricci-flat and asymptotically flat, just Ricci-flat, or Ricci non-flat. In each situation a number of quality factors are constructed and analysed. The relevance of these quality factors is clear in any situation where one seeks a rigorous formulation of the statement that a space-time is “close” to the Kerr solution, such as: its non-linear stability problem, the asymptotic settlement of a radiating isolated system undergoing gravitational collapse, or in the formulation of some uniqueness results.     

A class of exact solutions for coupled electromagnetic and scalar fields for einstein-rosen metric. II

This paper is a continuation of the author's earlier work entitled “A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. I.” [Ann. Physics69 (1972), 473]. In this paper we have interpreted some of the solutions from different viewpoints with special reference to singular behavior. It has been observed that the presence of zero mass scalar meson fields does not affect the singular behavior as when the electromagnetic field only is present.     

Dual invariant theory. Renormalization. Models

The problem of renormalization of a dual-Invariant theory of massive charged vector particles is considered for the case of electromagnetic interactions. A model of weak interactions is suggested, in which particles described by the dual-invariant theory play the role of intermediate vector bosons. Renormalizability and unitarity of the model are shown.     

Local relativistic invariant flows for quantum fields

For quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the Lorentz group by automorphisms on a Banach space generated by the Weyl algebra.     

Static and stationary axially symmetric gravitational fields of bounded sources. I. Solutions obtainable from the van Stockum metric

This paper shows that a new class of axially symmetric static electrovacuum solutions and the Kerr solution are obtainable from the van Stockum metric. The new class contains an infinite set of asymptotically flat solutions (in closed form), each of which involves an arbitrary set of parameters. The parameters have to be interpreted as functions of massm, chargee, and higher electric multipole moments _i of the particle. The casee= _i =0 leads to the Darmois metric. Well-known and new examples are given.     

A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. Part IA

In the previous work [1] we have obtained a class of exact solutions for the nonstatic cylindrically symmetric Einstein-Rosen metric in the presence of combined electromagnetic and zero-rest-mass scalar meson fields. But, these solutions are restricted because of assuming certain conditions on the scalar field. The present work deals with all the solutions obtained in the previous paper without any such restriction. The class of exact solutions obtained thus is more general than that given in [1].     

A planar perturbation of the Bianchi type I metric

The standard procedure for finding analytic perturbations in General Relativity suffers from the drawback that it is cumbersome to use beyond linear order perturbations. Following up on our previous work, we continue to use an alternate method of finding perturbations. We find a plane symmetric perturbation of the cosmological Bianchi type I metric. The perturbation corresponds to a fluid with heat flow moving perpendicularly to a singular plane in a region which can be made to be either overdense or underdense relative to the background spacetime. The fluid satisfies both the Strong and Dominant energy conditions everywhere except the region close to the singularity.     

Stationary vacuum fields with a conformally flat three-space I. General theory

A generalized notion of conformastat space-times is introduced in relativity theory. In this sense, the conformastat space-time is stationary with the three-space of timelike Killing trajectories being conformally flat. A 3+1 decomposition of the field equations is given, and two classes of nonstatic conformastat vacuum fields are exhaustively investigated. The resulting three metrics form a NUT-type extension of the solution of the static conformastat vacuum problem. We conjecture that all conformastat vacuum space-times are axially symmetric.