scholarly journals Light field integration in SUGRA theories

2015 ◽  
Vol 30 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Diego Gallego
Keyword(s):  
Analytic Continuation ◽  
Configuration Space ◽  
Light Field ◽  
Equations Of Motion ◽  
Invariant Function ◽  
Field Configuration ◽  
Effective Theory ◽  
Gauge Symmetries ◽  
The One ◽  
Breaking Scale

We revisit the integration of fields in 𝒩 = 1 Supergravity with the requirement that the effective theory has a reliable two-derivative supersymmetric description. In particular, we study, in a supersymmetric manifest way, the situation where the fields that are mapped out have masses comparable to the Supersymmetry breaking scale and masses of the remaining fields. We find that as long as one stands in regions of the field configuration space where the analytic continuation to superspace of the F-flatness conditions be reliable equations of motion for the fields that are being mapped out, and provided their solutions are stable regardless the dynamics of the remaining fields, such a two-derivative description is a reliable truncation of the full effective theory. The study is mainly focused to models with two chiral sectors, H and L, described by a Kähler invariant function with schematic dependencies of the form [Formula: see text], which leads to a nearly decoupled theory that allows the previous requirements to be easily satisfied in a consistent way. Interestingly, enough for the matters of our study, this kind of models present a scenario that is as safe as the one presented in sequestered models. It is also possible to allow gauge symmetries as long as these appear also factorized in hidden and visible sectors. Then, the integration of the hidden vector superfields is compulsory and proceeds reliably through the D-flatness condition analytically continued to superspace.

scholarly journals Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1430
Author(s):  
Fernando Barbero ◽  
Marc Basquens ◽  
Valle Varo ◽  
Eduardo J. S. Villaseñor
Keyword(s):  
General Relativity ◽  
Configuration Space ◽  
Equations Of Motion ◽  
Manifolds With Boundary ◽  
Test Bed ◽  
Hamiltonian Description ◽  
Gravitational Theories ◽  
The One ◽  
Direct Use ◽  
Singular Lagrangians

The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals The Spin Structure of the Nucleon

2016 ◽  
Vol 40 ◽  
pp. 1660001
Author(s):  
Xiangdong Ji ◽  
Yong Zhao
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Proton Spin ◽  
Effective Theory ◽  
Large Momentum ◽  
Theory Approach ◽  
The One ◽  
The Relationship

We justify the physical meaning of the spin and orbital angular momentum of free partons in the infinite momentum frame, and discuss the relationship between the Jaffe-Manohar and Ji’s sum rules for proton spin. The parton orbital angular momentum in the Jaffe-Manohar sum rule can be measured through twist-three GPD’s in hard scattering processes such as deeply virtual Compton scattering. Furthermore, we propose that the paton orbital angular momentum as well as the gluon helicity can be calculated in lattice QCD through a large momentum effective theory approach, and provide all the one-loop matching conditions for the proton spin content in perturbative QCD.

scholarly journals Spontaneously Broken Gauge Symmetry in a Bose Gas with Constant Particle Number

2017 ◽  
Vol 16 (01) ◽  
pp. 1750009
Author(s):  
A. Schelle
Keyword(s):  
Gauge Symmetry ◽  
Particle Number ◽  
Present Model ◽  
Phase Distribution ◽  
Equations Of Motion ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Gauge Symmetries ◽  
Non Local ◽  
Bose Einstein

The interplay between spontaneously broken gauge symmetries and Bose–Einstein condensation has long been controversially discussed in science, since the equations of motion are invariant under phase transformations. Within the present model, it is illustrated that spontaneous symmetry breaking appears as a non-local process in position space, but within disjoint subspaces of the underlying Hilbert space. Numerical simulations show that it is the symmetry of the relative phase distribution between condensate and non-condensate quantum fields which is spontaneously broken when passing the critical temperature for Bose–Einstein condensation. Since the total number of gas particles remains constant over time, the global U(1)-gauge symmetry of the system is preserved.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

scholarly journals Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 226
Author(s):  
Maricel Agop ◽  
Mitică Craus
Keyword(s):  
Complex System ◽  
Fractal Theory ◽  
Invariant Function ◽  
Hydrodynamic Type ◽  
Simultaneous Action ◽  
Systems Dynamics ◽  
Invariant Functions ◽  
Scale Relativity ◽  
The One ◽  
Joint Invariant

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved.

scholarly journals Physical and Mathematical Fluid Mechanics

Water ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 2199
Author(s):  
Markus Scholle
Keyword(s):  
Fluid Mechanics ◽  
Continuum Hypothesis ◽  
Equations Of Motion ◽  
Local Equilibrium ◽  
Physical Modelling ◽  
Mathematical Methods ◽  
Open Questions ◽  
Software Codes ◽  
The One ◽  
The Continuum

Fluid mechanics has emerged as a basic concept for nearly every field of technology. Despite there being a well-developed mathematical theory and available commercial software codes, the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved, and there are still open questions regarding the underlying physics of fluid flow, especially with respect to the continuum hypothesis and thermodynamic local equilibrium. The aim of this Special Issue is to reference recent advances in the field of fluid mechanics both in terms of developing sophisticated mathematical methods for finding solutions of the equations of motion, on the one hand, and on novel approaches to the physical modelling beyond the continuum hypothesis and thermodynamic local equilibrium, on the other.

scholarly journals Electron acceleration in underdense plasmas described with a classical effective theory

2015 ◽  
Vol 33 (2) ◽  
pp. 307-313 ◽  
Author(s):  
M. A. Pocsai ◽  
S. Varró ◽  
I. F. Barna
Keyword(s):  
Experimental Data ◽  
Continuous Medium ◽  
Equations Of Motion ◽  
Electron Acceleration ◽  
Index Of Refraction ◽  
Effective Theory ◽  
Electron Motion ◽  
Particle In Cell ◽  
Underdense Plasmas ◽  
Relativistic Equations

AbstractAn effective theory of laser–plasma-based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction nm in which a single electron propagates. Because of the simplicity of this model, we did not perform particle-in-cell (PIC) simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analyzed. We compared our results with PIC simulations and experimental data.

Noether gauge symmetries of geodesic motion in stationary and nonstatic Gödel-type spacetimes

2015 ◽  
Vol 38 ◽  
pp. 1560072 ◽  
Author(s):  
Ugur Camci
Keyword(s):  
Equations Of Motion ◽  
Complete Characterization ◽  
First Integrals ◽  
Geodesic Motion ◽  
Geodesic Equations ◽  
Gauge Symmetries ◽  
Geodesic Equations Of Motion

In this study, we obtain Noether gauge symmetries of geodesic motion for geodesic Lagrangian of stationary and nonstatic Gödel-type spacetimes, and find the first integrals of corresponding spacetimes to derive a complete characterization of the geodesic motion. Using the obtained expressions for [Formula: see text] of each spacetimes, we explicitly integrate the geodesic equations of motion for the corresponding stationary and nonstatic Gödel-type spacetimes.

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

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