scholarly journals Local symmetries and physical degrees of freedom in f(T) gravity: A Dirac-Hamiltonian constraint analysis

2020 ◽  
Vol 102 (6) ◽  
Author(s):  
Milutin Blagojević ◽  
James M. Nester
Keyword(s):  
Degrees Of Freedom ◽  
Hamiltonian Constraint ◽  
Constraint Analysis ◽  
Local Symmetries ◽  
Dirac Hamiltonian

scholarly journals The Hamiltonian dynamics of Hořava gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Deniz O. Devecioğlu ◽  
Mu-In Park
Keyword(s):  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Hamiltonian Formulation ◽  
Hamiltonian Constraint ◽  
Dirac Bracket ◽  
Constraint Analysis ◽  
Horava Gravity ◽  
Dynamical Consistency ◽  
Dynamical Degrees ◽  
Additional Phase

Abstract We consider the Hamiltonian formulation of Hořava gravity in arbitrary dimensions, which has been proposed as a renormalizable gravity model for quantum gravity without the ghost problem. We study the full constraint analysis of the non-projectable Hořava gravity whose potential, $$\mathcal{V}(R)$$V(R), is an arbitrary function of the (intrinsic) Ricci scalar R but without the extension terms which depend on the proper acceleration $$a_i$$ai. We find that there exist generally three distinct cases of this theory, A, B, and C, depending on (i) whether the Hamiltonian constraint generates new (second-class) constraints or just fixes the associated Lagrange multipliers, or (ii) whether the IR Lorentz-deformation parameter $${\lambda }$$λ is at the conformal point or not. It is found that, for Cases A and C, the dynamical degrees of freedom are the same as in general relativity, while, for Case B, there is one additional phase-space degree of freedom, representing an extra (odd) scalar graviton mode. This would achieve the dynamical consistency of a restricted model at the fully non-linear level and be a positive result in resolving the long-standing debates about the extra graviton modes of the Hořava gravity. Several exact solutions are also studied as some explicit examples of the new constraints. The structure of the newly obtained, “extended” constraint algebra seems to be generic to Hořava gravity and its general proof would be a challenging problem. Some other challenging problems, which include the path integral quantization and the Dirac bracket quantization are discussed also.

REVIEW OF RECENT DEVELOPMENTS IN SUPERSTRING THEORY

1987 ◽  
Vol 02 (03) ◽  
pp. 593-643 ◽  
Author(s):  
JOHN H. SCHWARZ
Keyword(s):  
Degrees Of Freedom ◽  
Classical Solutions ◽  
Type Ii ◽  
World Sheet ◽  
Superstring Theory ◽  
Recent Developments ◽  
Local Symmetries ◽  
Superconformal Theories ◽  
Superstring Theories ◽  
Internal Degrees Of Freedom

After proposing a procedure for classifying string theories, we describe the various local symmetries that can occur on the world sheet with special emphasis on Kac–Moody algebras in superconformal theories. The construction of multiloop amplitudes is briefly reviewed. Then the constraint of modular invariance is analyzed for models in which the internal degrees of freedom are described by fermions. Next we consider the construction of consistent classical solutions. A few examples are presented for both the heterotic and type II superstring theories. A brief description of some recent work in string field theory and other approaches to a nonperturbative formulation of string theory is presented.

scholarly journals Holonomy and inverse-triad corrections in spherical models coupled to matter

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Asier Alonso-Bardaji ◽  
David Brizuela
Keyword(s):  
General Relativity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Vacuum Model ◽  
Symmetric Spacetimes ◽  
Starting Point ◽  
Spherical Models ◽  
Matter Fields

AbstractLoop quantum gravity introduces two characteristic modifications in the classical constraints of general relativity: the holonomy and inverse-triad corrections. In this paper, a systematic construction of anomaly-free effective constraints encoding such corrections is developed for spherically symmetric spacetimes. The starting point of the analysis is a generic Hamiltonian constraint where free functions of the triad and curvature components as well as non-minimal couplings between geometric and matter degrees of freedom are considered. Then, the requirement of anomaly freedom is imposed in order to obtain a modified Hamiltonian that forms a first-class algebra. In this way, we construct a family of consistent deformations of spherical general relativity, which generalizes previous results in the literature. The discussed derivation is implemented for vacuum as well as for two matter models: dust and scalar field. Nonetheless, only the deformed vacuum model admits free functions of the connection components. Therefore, under the present assumptions, we conclude that holonomy corrections are not allowed in the presence of these matter fields.

scholarly journals Hybrid models in loop quantum cosmology

2016 ◽  
Vol 25 (08) ◽  
pp. 1642007 ◽  
Author(s):  
Beatriz Elizaga Navascués ◽  
Mercedes Martín-Benito ◽  
Guillermo A. Mena Marugán
Keyword(s):  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Hybrid Approach ◽  
Loop Quantum Cosmology ◽  
Hamiltonian Constraint ◽  
Hybrid Strategy ◽  
Fock Representation ◽  
Zero Modes ◽  
Inhomogeneous Models ◽  
Global Zero

In the framework of Loop Quantum Cosmology (LQC), inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid LQC.

scholarly journals Spin jumping in the context of a QCD effective model

2017 ◽  
Vol 32 (06n07) ◽  
pp. 1750041
Author(s):  
G. B. de Gracia
Keyword(s):  
Equations Of Motion ◽  
Point Of View ◽  
Effective Theory ◽  
Tree Level ◽  
Hamiltonian Constraint ◽  
Constraint Analysis ◽  
Antisymmetric Tensor Field ◽  
Massive Phase ◽  
Tensor Formulation ◽  
Quantum Point

The tensor formulation for the effective theory of QCD vector resonances, whose model we denote by TEVR, is given by an antisymmetric tensor field and describes spin 1 particles. Our goal is to show, by different approaches, that the Abelian version of this model presents the so-called “spin jumping” when we consider its massless limit. Classically we find, by the use of the equations of motion and the Hamiltonian constraint analysis, that the massive phase of the model describes spin 1 particles while its massless phase describes spin 0 particles. From the quantum point of view, we derive these conclusions via tree-level unitarity analysis and the master action approach.

Mobility and singularity analyses of a symmetric multi-loop mechanism for space applications

2021 ◽  
pp. 095440622199555
Author(s):  
Chuanyang Li ◽  
Jorge Angeles ◽  
Hongwei Guo ◽  
Huiyin Yan ◽  
Dewei Tang ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Space Applications ◽  
Aerospace Applications ◽  
Constraint Analysis ◽  
Multi Stage ◽  
Prismatic Joints ◽  
The Subject ◽  
Three Degrees Of Freedom

A symmetric, double-tripod multi-loop mechanism (DTMLM), for aerospace applications, is the subject of this paper. Its mobility and singularity are analyzed, while introducing a novel tool, the cell-division method for singularity analysis, applicable to multi-loop mechanisms. The key principle of this method lies in replacing the singularity analysis of the original multi-loop mechanism with: (1) that of an equivalent simpler parallel mechanism; (2) the constraint analysis between loops; and (3) the singularity analysis of simpler kinematic subchains. Then, the mechanism is transformed into a simpler, equivalent parallel mechanism with three identical kinematic subchains. Its mobility and singularity are analyzed based on screw algebra, which leads to a key conclusion about the geometric properties of this mechanism. Results show that: (a) the DTMLM has three degrees of freedom (dof), i.e., two rotational dof around two intersecting axes lying in the middle plane of the mechanism, and one translational dof along the normal to the said plane (2R1T); and (b) the singularities of the 3-RSR parallel mechanism are avoided in the DTMLM by means of prismatic joints, singularities in the DTMLM occurring on the boundary of its workspace. Thus, the DTMLM has a 2R1T mobility everywhere within its workspace. When a set of multi-loop mechanisms of this kind are stacked as modules to assemble a multi-stage manipulator for space applications, the modules can be designed so that, under paradigm operations, all individual loops operate within their workspace, safe from singularities.

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.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

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