scholarly journals A model for massless higher spin field interacting with a geometrical background

2015 ◽  
Vol 12 (05) ◽  
pp. 1550054
Author(s):  
Giuseppe Bandelloni
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Theory Model ◽  
Algebraic Field ◽  
Spin Field ◽  
Higher Spin ◽  
A Chain ◽  
Equations Of Motions

We study a very general four-dimensional field theory model describing the dynamics of a massless higher spin N symmetric tensor field particle interacting with a geometrical background. This model is invariant under the action of an extended linear diffeomorphism. We investigate the consistency of the equations of motion, and the highest spin degrees of freedom are extracted by means of a set of covariant constraints. Moreover, the highest spin equations of motions (and in general all the highest spin field 1-PI irreducible Green functions) are invariant under a chain of transformations induced by a set of N - 2 Ward operators, while the auxiliary fields equations of motion spoil this symmetry. The first steps to a quantum extension of the model are discussed on the basis of the algebraic field theory. Technical aspects are reported in Appendices, in particular, one of them is devoted to illustrate the spin-2 case.

UNCONSTRAINED HIGHER SPINS IN FOUR DIMENSIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 511-556 ◽  
Author(s):  
GIUSEPPE BANDELLONI
Keyword(s):  
Equations Of Motion ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Geometrical Meaning ◽  
Four Dimensions ◽  
Spin Field ◽  
Angular Momenta ◽  
Higher Spin ◽  
Spin Fields ◽  
The Right

The relativistic symmetric tensor fields are, in four dimensions, the right candidates to describe Higher Spin Fields. Their highest spin content is isolated with the aid of covariant conditions, discussed within a group theory framework, in which auxiliary fields remove the lower intrinsic angular momenta sectors. These conditions are embedded within a Lagrangian Quantum Field theory which describes an Higher Spin Field interacting with a Classical background. The model is invariant under a (B.R.S.) symmetric unconstrained tensor extension of the reparametrization symmetry, which include the Fang–Fronsdal algebra in a well defined limit. However, the symmetry setting reveals that the compensator field, which restore the Fang–Fronsdal symmetry of the free equations of motion, is in the existing in the framework and has a relevant geometrical meaning. The Ward identities coming from this symmetry are discussed. Our constraints give the result that the space of the invariant observables is restricted to the ones constructed with the Highest Spin Field content. The quantum extension of the symmetry reveals that no new anomaly is present. The role of the compensator field in this result is fundamental.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Elements of Classical Field Theory

2021 ◽  
pp. 24-34
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Classical Field ◽  
Lagrange Equations ◽  
Lie Group Of Transformations ◽  
Infinitesimal Transformations ◽  
Conserved Currents

The purpose of this chapter is to recall the principles of Lagrangian and Hamiltonian classical mechanics. Many results are presented without detailed proofs. We obtain the Euler–Lagrange equations of motion, and show the equivalence with Hamilton’s equations. We derive Noether’s theorem and show the connection between symmetries and conservation laws. These principles are extended to a system with an infinite number of degrees of freedom, i.e. a classical field theory. The invariance under a Lie group of transformations implies the existence of conserved currents. The corresponding charges generate, through the Poisson brackets, the infinitesimal transformations of the fields as well as the Lie algebra of the group.

scholarly journals The masses of gauge fields in higher spin field theory on the bulk of AdS4

2005 ◽  
Vol 613 (3-4) ◽  
pp. 197-207 ◽  
Author(s):  
Ruben Manvelyan ◽  
Werner Rühl
Keyword(s):  
Field Theory ◽  
Gauge Fields ◽  
Spin Field ◽  
Higher Spin ◽  
The Masses

scholarly journals Graviton-mediated scattering amplitudes from the quantum effective action

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Tom Draper ◽  
Benjamin Knorr ◽  
Chris Ripken ◽  
Frank Saueressig
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Effective Action ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Explicit Construction ◽  
Effective Field ◽  
Quantum Corrections ◽  
Higher Spin ◽  
Infinite Derivative

Abstract We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.

scholarly journals The Higgs mechanism in nonlocal field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Higgs Mechanism ◽  
Local Theory ◽  
Perturbative Order ◽  
Local Field Theory ◽  
Nonlocal Field Theory ◽  
Nonlocal Action ◽  
Nonlocal Field

Abstract We provide an example of nonlocal scalar electrodynamics that allows the same Higgs mechanism so successful in local field theory. The nonlocal action is structured in order to have the same exact solutions and the same equations of motion for perturbations of the local theory, at any perturbative order. Therefore, the perturbative degrees of freedom that propagate in the unstable vacuum are reshuffled when the stable vacuum is replaced in the EoM, but their number does not change at any perturbative order, and their properties are the same like in the usual local theory. Finally, the theory is superrenormalizable or finite at quantum level.

Formulation of Equations of Motion for a Chain of Flexible Links Using Hamilton’s Principle

1994 ◽  
Vol 116 (1) ◽  
pp. 81-88 ◽  
Author(s):  
M. Benati ◽  
A. Morro
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamic Equations ◽  
Relative Deformation ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Flexible Links ◽  
A Chain

The dynamic equations of a chain of flexible links are determined by means of Hamilton’s principle. First a continuous model is adopted and the boundary conditions are determined, along with the partial differential equations of motion. Then a model with a finite number of degrees of freedom is set up. The configuration of each link is described through the line which joins the end points and the relative deformation is described in terms of appropriate trial functions. The boundary conditions are incorporated into a set of basic trial functions. The time-dependent coefficients of the remaining shape functions play the role of Lagrangian coordinates. The dynamic equations are then derived and the procedure is contrasted with other methods for reduction of a system of links to a system with a finite number of degrees of freedom.

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