Spinning strings of the Neveu-Schwarz-Ramond type in 3, 4, 6, and 10 space-time dimensions

1999 ◽  
Vol 77 (6) ◽  
pp. 427-446
Author(s):  
S B Phillips
Keyword(s):  
Degrees Of Freedom ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Physical Space ◽  
Space Time ◽  
Coordinate Space ◽  
Time Dimension ◽  
Light Cone Gauge ◽  
Fermionic Sector

A model of a spinning string with an internal coordinate index is proposed and studied. When the action for this model is taken to be diagonal in this internal coordinate space and quantized in the light-cone gauge it is found to be Lorentz covariant in four-dimensional space-time provided that the internal coordinate space is four dimensional.This combination of space-time dimension, D, and internal coordinate space dimension, N, is just one of four possible sets, the other three corresponding to D = 3, 6, and 10, precisely the same values for which it is possible to formulate Yang-Mills theories with simple supersymmetry. By comparing the number of propagating degrees of freedom at the zero-mass level in the open string bosonic and fermionic sectors it is found that a supersymmetric interpretation of this model is possible provided that all physical states in the bosonic sector have even G-parity and the ground-state spin or in the fermionic sector have positive chirality. A possible interpretation of the connection betweenthe N components of each of the D space-time coordinates is presentedon the basis that the space-time coordinates are scalars in the internal coordinate space. This interpretation would appear to be reasonable given the fact that the field variables in the Lagrangian density do not necessarily have to represent physically measurable quantities but can, instead, only represent physically measurable quantities when combined in some manner, the simplest of which being a linear combination. The Lagrangian density simply produces the equations of motion and the constraint equations for the independent variables, only linear combinations of which represent the four dimensions of physical space-time.PACS Nos.: 11.17.+y, 11.10.Qr, 1.30.Cp, 11.30.Pb

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

scholarly journals Lorentz-violating effects in three-dimensional QED

2014 ◽  
Vol 29 (22) ◽  
pp. 1450112 ◽  
Author(s):  
R. Bufalo
Keyword(s):  
Quantum Electrodynamics ◽  
Lagrangian Density ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Nonminimal Coupling ◽  
Coupling Term ◽  
Interaction Terms ◽  
Higher Derivative ◽  
Dimensional Space Time

Inspired in discussions presented lately regarding Lorentz-violating interaction terms in B. Charneski, M. Gomes, R. V. Maluf and A. J. da Silva, Phys. Rev. D86, 045003 (2012); R. Casana, M. M. Ferreira Jr., R. V. Maluf and F. E. P. dos Santos, Phys. Lett. B726, 815 (2013); R. Casana, M. M. Ferreira Jr., E. Passos, F. E. P. dos Santos and E. O. Silva, Phys. Rev. D87, 047701 (2013), we propose here a slightly different version for the coupling term. We will consider a modified quantum electrodynamics with violation of Lorentz symmetry defined in a (2+1)-dimensional space–time. We define the Lagrangian density with a Lorentz-violating interaction, where the space–time dimensionality is explicitly taken into account in its definition. The work encompasses an analysis of this model at both zero and finite-temperature, where very interesting features are known to occur due to the space–time dimensionality. With that in mind, we expect that the space–time dimensionality may provide new insights about the radiative generation of higher-derivative terms into the action, implying in a new Lorentz-violating electrodynamics, as well the nonminimal coupling may provide interesting implications on the thermodynamical quantities.

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

scholarly journals Transient Annular Structures in Exploding Galaxies

1972 ◽  
Vol 44 ◽  
pp. 313-313
Author(s):  
J. L. Sěrsic
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Relative Velocity ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Physical Space ◽  
Space Time ◽  
High Mass ◽  
New Variables

The explosive events going on in the central parts of some galaxies are related to a very high mass concentration. As an explosion is actually a drastic rearrangement of the concerned masses with energy release, the binding energy of the central core will change and, correspondingly, its effective gravitational mass. A test particle far from the nuclear region, although within the galaxy, will be moving accordingly in a variable-mass Newtonian gravitational field.On the other hand the observations suggest that explosions in galaxies have axial symmetry, so we are concerned with the global properties of the motion of a particle in a variable mass axisymmetric gravitational field. In order to get rid of the mass variation a space-time conformal transformation is made, which, after imposing some not very restrictive conditions, leads to a conservative potential in the new variables. This new potential has additional terms due to the elimination of the variable mass. The equations of motion in the new variables provide the motion of the test particle relative to an expanding or contracting background which depends on the choice of the transformation and the law of the mass variability. The problem is, at this point, formally similar to Hill's. It is possible to write an equation for the relative energy (a generalization of Jacobi's integral) and also to define surfaces of zero relative velocity for the infinitesimal particle. The general topological properties of these surfaces require singular points along the symmetry axis (analogous to the collinear Eulerian points) and also a dense set in a circumference on a plane perpendicular to the symmetry axis (analogous to the Lagrangian points). The latter one is the main feature characterizing the topology of the zero relative velocity surfaces. Even when we lift some of the restrictive conditions, the Lagrangian ring preserves its properties, as for example, the one of being the only region where zero-velocity curves and equi-potentials coincide when the configuration evolves in time (in the transformed space-time).It is easy to understand that the topology of the surfaces is kept when we reverse the transformation and go back to physical space-time. If the dust, gas or stars in the system has definite upper limits for its Jacobian constants, spatial segregation of them will arise, as is the case in radio-galaxies such as NGC 5128, NGC 1316, etc. where ringlike dust structures are observed.

scholarly journals THE LOW ENERGY EFFECTIVE LAGRANGIAN FOR PHOTON INTERACTIONS IN ANY DIMENSION

1996 ◽  
Vol 11 (02) ◽  
pp. 253-269 ◽  
Author(s):  
A. RITZ ◽  
R. DELBOURGO
Keyword(s):  
Dimensional Space ◽  
Effective Interaction ◽  
Bernoulli Polynomial ◽  
Weak Field ◽  
Space Time ◽  
Low Energy ◽  
Time Dimension ◽  
Effective Lagrangian ◽  
Dimensional Space Time ◽  
Photon Interactions

The subject of low energy photon-photon scattering is considered in arbitrary-dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalization resolves the structure of the weak field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related not only to the space-time dimension but also to the coefficients of the Bernoulli polynomial.

scholarly journals QUANTIZATION OF BOSONIC STRING MODEL IN (26+2)-DIMENSIONAL SPACE–TIME

2004 ◽  
Vol 19 (12) ◽  
pp. 1923-1959 ◽  
Author(s):  
TAKUYA TSUKIOKA ◽  
YOSHIYUKI WATABIKI
Keyword(s):  
Dimensional Space ◽  
String Model ◽  
Space Time ◽  
Bosonic String ◽  
World Sheet ◽  
Light Cone Gauge ◽  
Weyl Invariance ◽  
Background Space ◽  
Dimensional Space Time ◽  
Gauge Formulation

We investigate the quantization of the bosonic string model which has a local U (1) V × U (1) A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations á la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in (26+2)-dimensional background space–time involving two time-like coordinates.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

scholarly journals Dynamical Codimension – 2 Brane in a Warped Six Dimensional Space-time

2018 ◽  
Vol 28 (3) ◽  
pp. 277
Author(s):  
Phan Hong Lien
Keyword(s):  
Einstein Equation ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Cosmological Evolution ◽  
System Of Equations ◽  
Dimensional Space Time ◽  
Six Dimensions ◽  
Bulk Space

In this paper we present the Einstein equation extended in six-dimensions (6D) from the formation of codimension-2 brane, which is created by a 4-brane and 4-anti brane moving in the warped 6D “bulk” space-time. The system of equations of motion for the dynamical codimension - 2 brane has been derived to describe the cosmological evolution on the probe branes. Some cosmological consequences are investigated.

Some properties of the p-brane model with the quadratic lagrangian

1999 ◽  
Vol 4 ◽  
pp. 97-112
Author(s):  
P. Miškinis
Keyword(s):  
Dimensional Space ◽  
Equations Of Motion ◽  
Critical Dimension ◽  
Space Time ◽  
Brane Model ◽  
Arbitrary Topology ◽  
General Properties ◽  
Dimensional Space Time ◽  
Dimensional Surface

Some general properties of the relativistic p-dimensional surface imbedded into D-dimensional space-time and its reduction to the simplest case of the quadratic Lagrangian are considered. The solutions of the equations of motion of such model for the p-brane with arbitrary topology and massless eigenstates, as well as with critical dimension after quantization are presented. Some generalizations for the supermembrane are discussed.

Sign in / Sign up

Export Citation Format

Share Document