Nambu String Research Articles

Quantum viewpoint of quadratic f(R) gravity, constraints, vacuum-to-vacuum transition amplitude and particle content

We investigate, from a quantum viewpoint, the nature of the linearized quadratic \(f(R)=(R+aR^2)\)-gravity. To derive the explicit expression of the underlying propagator of the theory, the field is coupled to an external energy–momentum \(T^{\mu \nu }\), and an auxiliary field is introduced to deal with gauge constraints as done in gauge theories. In particular for a conserved \(T^{\mu \nu }\), we establish the gauge invariance of the vacuum-to-vacuum transition amplitude \(\langle 0_+|0_-\rangle \), and prove the necessary positivity condition \(|\langle 0_+|0_-\rangle |^2 0\), required by the quantum theory aspect of the treatment. An exact expression is then derived of the number of particles emitted, at a given energy, by a circularly oscillating Nambu string from which we may compare the relative number of the spin 0 massive particles emitted to the graviton number which turns up to give a clear cut departure from the general relativity prediction.

Some exact solutions of magnetized viscous model in string cosmology

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.

Magnetized Viscous Fluid Anisotropic Models in String Cosmology

We study the evolution of a homogeneous and anisotropic Bianchi type VI0 cosmological model in the presence of magnetic field and viscous fluid together with a cloud of cosmic strings in general relativity. Since Viscous fluid and magnetic field have cosmological origin, it is interesting to discuss the effects of viscous fluid and magnetic field on the expansion history of the universe in early and later stages of evolution in string cosmol- ogy. Exact solutions of the field equations are obtained using the equation of state for a cloud of strings. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. The two string models, namely, geometrical(Nambu string) and Takabayasi (p-string) string models are discussed with magnetized and non-magnetized viscous fluid by taking certain physical conditions. We also examine numerically the effects of bulk viscosity and magnetic field on potential in each string model. We find that magnetic field and viscous fluid play important role during the early evolution of the universe. We observe that the viscous term affects the evolution much rapid as compare to magnetic field. The presence of viscous term prevents the universe to be empty. The other physical and geometrical aspects of each string model are also discussed in detail.

String cosmology in LRS Bianchi type-II dusty Universe with time-decaying vacuum energy density Λ

A model of a cloud formed by massive strings is used as a source of LRS Bianchi type II with time decaying vacuum energy density $\Lambda$. To construct string cosmological models we have used the energy-momentum tensor for such string as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings, (i) Massive string and (ii) Nambu string. The expansion $\theta$ in the model is assumed to be proportional to the shear $\sigma$. This condition leads to $A=\beta B^{m}$, where $A$ and $B$ are the metric coefficients, $m$ is a constant and $\beta$ is an integrating constant. Our models are in accelerating phase which is consistent to the recent observations of supernovae type Ia. The physical and geometrical behavior of these models are also discussed.

The rest-frame instant form and Dirac observables for the open Nambu string

The rest-frame instant form of the positive-energy part of the open Nambu string is developed. The string is described as a decoupled non-local canonical non-covariant Newton-Wigner center of mass plus a canonical basis of Wigner-covariant relative variables living in the Wigner 3-spaces. The center of mass carries a realization of the Poincaré algebra depending upon the invariant mass and the rest-spin of the string, functions of the relative variables. A canonical basis of gauge-invariant Dirac observables is built with Frenet-Serret geometrical methods. Some comments on canonical quantization are made.

Magnetized Bianchi Type III Massive String Cosmological Models in General Relativity

The present study deals with Bianchi type III string cosmological models with magnetic field. The magnetic field is assumed to be along z direction. Therefore F 12 is only the non-vanishing component of electromagnetic field tensor F ij . The expansion (θ) in the model is assumed to be proportional to the shear (σ). To get determinate solution in term of cosmic time, we have solved the fields equations in two cases (i) Reddy and (ii) Nambu string. The physical and geometrical behaviour of these models is discussed.

Cosmic Strings and Domain Walls in a Scale-Covariant Theory of Gravitation

Axially symmetric space-time is considered in the presence of cosmic string source and thick domain walls in the frame work of a scale-covariant theory of gravitation. A relation between metric potential is assumed to get a determinate solution of the field equations of this theory. In this particular case, it is observed that the geometric (Nambu) string p-string (Takabayasi string) and Reddy string do not survive. It is also seen that the stiff (self-gravitating) domain walls do not exist in this theory.

Higher-dimensional knotlike topological defects in local non-Abelian topological tensor currents

We present the novel topological tensor currents to describe the infinitesimal thin higher-dimensional topological defects in the local SO(n) gauge theory. The topological quantization of defects and the inner structure of the currents are obtained. As the generalization of Nielsen-Olesen local U(1) field theory for Nambu string, the local SO(n) gauge-invariant Lagrangian and the motion equation of the higher-dimensional topological defects are derived. Moreover, for closed defects, we study their important topological configuration, i.e., the higher-dimensional knotlike structures. Using the topological tensor currents and their preimages, we construct a series of metric independent integrals and prove their gauge independence. Similar to the helicity integral characterizing one-dimensional knotlike vortex filament, these topological invariants are evaluated to the generalized linking numbers of higher-dimensional knotlike defects.

A Xially Symmetric Cosmic Strings and Domain Walls in Lyra Geometry

Axially symmetric space time is considered in the presence of cosmic string source and thick domain walls in the frame work of Lyra (1951) geometry. Exact cosmological models, which represent geometric (Nambu) string and stiff domain walls are presented. It is interesting to note that the cosmological models, obtained in both the cases, are identical. Some physical and kinematical properties of the models are discussed.

STRING COSMOLOGY WITH MAGNETIC FIELD IN BIANCHI V MODEL

String Cosmology with magnetic field has been studied for Bianchi V space-time model for different directions of the magnetic field and string. For equation of state, we have examined geometric string (Nambu string), Takabayashi string (p-string), string with uniform energy density or barotropic equation of state. Exact analytic solution is possible only in few cases.

Particle Correlation in Quantum Field Theory. II

This is the second and last instalment of the investigation of particle correlation in quantum field theory for fundamental processes with two-mono-energetic particle productions. The angular correlation is defined as the average (epectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one that they tend to travel in opposing directions. The angular correlation of γγ produced in pair annihilation of charged particles in scalar quantum electrodynamics, scalar-pair production by charged and neutral Nambu strings, as well as e+e— pair-production by a Neutral Nambu string are studied in detail.

On Gravitational Radiation Graviton Number Density: Application to a Nambu String

A formalism is developed to compute the number density of gravitons, of specified energies, produced by an arbitrary external energy-momentum tensor source at any temperature. The formalism is applied to a simple Nambu string without making the usual assumption of a long wavelength approximation (L.W.A.). This exact result is also compared to the L.W.A.

Bosonization and current algebra of spinning strings

We write down a general geometric action principle for spinning strings in d-dimensional Minkowski space, which is formulated without the use of Grassmann coordinates. Instead, it is constructed in terms of the pull-back of a left invariant Maurer-Cartan form on the d-dimensional Poincaré group to the world-sheet. The system contains some interesting special cases. Among them are the Nambu string (as well as, null and tachyonic strings) where the spin vanishes, and also the case of a string with a spin current—but no momentum current. We find the general form for the Virasoro generators, and show that they are first class constraints in the Hamiltonian formulation of the theory. The current algebra associated with the momentum and angular momentum densities are shown, in general, to contain rather complicated anomaly terms which obstruct quantization. As expected, the anomalies vanish when one specializes to the case of the Nambu string, and there one simply recovers the algebra associated with the Poincaré loop group. We speculate that there exist other cases where the anomalies vanish, and that these cases give the bosonization of the known pseudoclassical formulations of spinning strings.

Fermion confinement by a relativistic flux tube.

We formulate the description of the dynamic confinement of a single fermion by a flux tube. The range of applicability of this model extends from the relativistic corrections of a slowly moving quark to the ultrarelativistic motion in a heavy-light meson. The reduced Salpeter equation, also known as the no-pair equation, provides the framework for our discussion. The Regge structure is that of a Nambu string with one end fixed. Numerical solutions are found giving very good fits to heavy-light meson masses. An Isgur-Wise function with a zero recoil slope of ${\ensuremath{\xi}}^{\ensuremath{'}}$(1)\ensuremath{\simeq}-1.26 is obtained. \textcopyright{} 1996 The American Physical Society.

Square-root actions, metric signature, and the path integral of quantum gravity.

We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand $\exp[ \sqrt{i} S ]$ rather than the familiar Feynman expression $\exp[ i S ]$, and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.

Fundamental constants and the problem of time.

We point out that for a large class of parametrized theories, there is a constant in the constrained Hamiltonian which drops out of the classical equations of motion in configuration space. Examples include the mass of a relativistic particle in free fall, the tension of the Nambu string, and Newton's constant for the case of pure gravity uncoupled to matter or other fields. In the general case, the classically irrelevant constant is proportional to the ratio of the kinetic and potential terms in the Hamiltonian. It is shown that this ratio can be reinterpreted as an {\it unconstrained} Hamiltonian, which generates the usual classical equations of motion. At the quantum level, this immediately suggests a resolution of the "problem of time" in quantum gravity. We then make contact with a recently proposed transfer matrix formulation of quantum gravity and discuss the semiclassical limit. In this formulation, it is argued that a physical state can obey a (generalized) Poincar\'e algebra of constraints, and still be an approximate eigenstate of 3-geometry. Solutions of the quantum evolution equations for certain minisuperspace examples are presented. An implication of our proposal is the existence of a small, inherent uncertainty in the phenomenological value of Planck's constant.

Large N solution of the 2D supersymmetric Yang-Mills theory

The Schwinger-Dyson equations of the Makeenko-Migdal type, when supplemented with some simple equations as a consequence of supersymmetry, form a closed set of equations for Wilson loops and related quantities in the two dimensional super-gauge theory. We solve these equations. It appears that the planar Wilson loops are described by the Nambu string without folds. We also discuss how to put the model on a spatial lattice, where a peculiar gauge is chosen in order to keep one supersymmetry on the lattice. Supersymmetry is unbroken in this theory. We comment on possible generalization of these considerations to other models.

The Lagrangian loop representation of lattice U(1) gauge theory

It is showed how the Hamiltonian lattice loop representation can be cast straighfforwardly in the Lagrangian formalism. The procedure is general and here we present the simplest case: pure compact QED. This connection has been shaded by the non canonical character of the algebra of the fundamental loop operators. The loops represent tubes of electric flux and can be considered the dual objects to the Nielsen-Olesen strings supported by the Higgs broken phase. The lattice loop classical action corresponding to the Villain form is proportional to the quadratic area of the loop world sheets and thus it is similar to the Nambu string action. This loop action is used in a Monte Carlo simulation and its appealing features are discussed.

The massive bosonic string in the center-of-mass gauge

The open Nambu string is revisited in the spirit of an early approach by Rohrlich. Strictly timelike motions only are considered. The proper-time of the center-of-mass is taken as preferred parameter. We propose a canonical formalism in terms of a countable infinity of variables, among them the modes. But the barycentric coordinates have noncommuting components, which makes possible a consistent quantization (in any dimension, four in particular) within the framework of a transverse space of states. If a maximal number of modes is further fixed, a transverse Hilbert space emerges, where spacetime displacements preserve the (positive-definite) scalar product.

Particle Correlation in Quantum Field Theory

The paper deals with studies of the angular correlation of two mono-energetic particles produced in several fundamental processes in quantum field theory. The angular correlation is defined as the average (expectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one indicates that they tend to travel in opposing directions. The angular correlations for photons and electrons produced by sources, and in quantum eletrodynamics, to lowest order, γγ produced in e+e− collision (annihilation), e+e− pair production in γγ collision, and finally e+e− pair production by a Nambu string are studied in detail.