scholarly journals Non-relativistic ten-dimensional minimal supergravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Lahnsteiner ◽  
L. Romano ◽  
J. Rosseel ◽  
C. Şimşek
Keyword(s):  
Equations Of Motion ◽  
Local Scale ◽  
Point Of View ◽  
Geometric Constraints ◽  
Relativistic Limit ◽  
Cartan Geometry ◽  
Yang Mills ◽  
The Poisson Equation ◽  
Minimal Supergravity ◽  
Supergravity Action

Abstract We construct a non-relativistic limit of ten-dimensional $$ \mathcal{N} $$ N = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.

scholarly journals A non-relativistic limit of NS-NS gravity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Lahnsteiner ◽  
L. Romano ◽  
J. Rosseel ◽  
C. Şimşek
Keyword(s):  
Scale Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Geometric Constraints ◽  
Target Space ◽  
Kinetic Term ◽  
Scale Invariant ◽  
Relativistic Limit ◽  
Cartan Geometry ◽  
Form Field

Abstract We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

scholarly journals Electron Trajectories in Molecular Orbitals

2020 ◽  
Author(s):  
Isaiah Sumner ◽  
Hannah Anthony
Keyword(s):  
Lagrange Multiplier ◽  
Equations Of Motion ◽  
Bohmian Mechanics ◽  
Molecular Orbitals ◽  
Quantum Hydrodynamics ◽  
Relativistic Limit ◽  
Quantum Particles ◽  
Quantum Force ◽  
Trajectory Methods ◽  
Structure Calculations

The time-dependent Schrödinger equation can be rewritten so that its interpretation is no longer probabilistic. Two well-known and related reformulations are Bohmian mechanics and quantum hydrodynamics. In these formulations, quantum particles follow real, deterministic trajectories influenced by a quantum force. Generally, trajectory methods are not applied to electronic structure calculations, since they predict that the electrons in a ground state, real, molecular wavefunction are motionless. However, a spin-dependent momentum can be recovered from the non-relativistic limit of the Dirac equation. Therefore, we developed new, spin-dependent equations of motion for the quantum hydrodynamics of electrons in molecular orbitals. The equations are based on a Lagrange multiplier, which constrains each electron to an isosurface of its molecular orbital, as required by the spin-dependent momentum. Both the momentum and the Lagrange multiplier provide a unique perspective on the properties of electrons in molecules.

scholarly journals Dark matter from non-relativistic embedding gravity

2021 ◽  
pp. 2150101
Author(s):  
S. A. Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Additional Contribution ◽  
Relativistic Limit ◽  
The Core ◽  
The Stability ◽  
Dimensional Surface

We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the [Formula: see text]CDM model.

UNUSUAL HYDRODYNAMICS

1987 ◽  
Vol 02 (05) ◽  
pp. 1591-1615 ◽  
Author(s):  
V.A. BEREZIN
Keyword(s):  
Black Hole ◽  
Cosmological Model ◽  
Production Process ◽  
Particle Production ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Point Of View ◽  
Modified Equations ◽  
Nonsingular Cosmological Model

A method for the phenomenological description of particle production is proposed. Correspondingly modified equations of motion and energy-momentum tensor are obtained. In order to illustrate this method we reconsider from the new point of view of (i) the C-field Hoyle-Narlikar cosmology, (ii) the influence of the particle production process on metric inside the event horizon of a charged black hole and (iii) a nonsingular cosmological model.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals COMPARATIVE STUDY OF VARIATIONAL CHAOS INDICATORS AND ODEs' NUMERICAL INTEGRATORS

2012 ◽  
Vol 22 (10) ◽  
pp. 1230033 ◽  
Author(s):  
L. A. DARRIBA ◽  
N. P. MAFFIONE ◽  
P. M. CINCOTTA ◽  
C. M. GIORDANO
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
General System ◽  
Detailed Comparison ◽  
Dynamical Problem ◽  
Point Of View ◽  
The Other ◽  
Numerical Integrators ◽  
Fast Lyapunov Indicator ◽  
The Times

The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of [Maffione et al., 2011b] for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of [Maffione et al., 2011b] for mappings to the 2D [Hénon & Heiles, 1964] potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical Spectra of Stretching Numbers (SSNs). We also include in the record the Relative Lyapunov Indicator (RLI), which is not a variational indicator as the others. Then, we test a numerical technique to integrate Ordinary Differential Equations (ODEs) based on the Taylor method implemented by [Jorba & Zou, 2005] (called taylor), and we compare its performance with other two well-known efficient integrators: the [Prince & Dormand, 1981] implementation of a Runge–Kutta of order 7–8 (DOPRI8) and a Bulirsch–Stöer implementation. These tests are run under two very different systems from the complexity of their equations point of view: a triaxial galactic potential model and a perturbed 3D quartic oscillator. We first show that a combination of the FLI/OFLI, the MEGNO and the GALI 2N succeeds in describing in detail most of the dynamical characteristics of a general Hamiltonian system. In the second part, we show that the precision of taylor is better than that of the other integrators tested, but it is not well suited to integrate systems of equations which include the variational ones, like in the computing of almost all the preceeding indicators of chaos. The result which induces us to draw this conclusion is that the computing times spent by taylor are far greater than the times consumed by the DOPRI8 and the Bulirsch–Stöer integrators in such cases. On the other hand, the package is very efficient when we only need to integrate the equations of motion (both in precision and speed), for instance to study the chaotic diffusion. We also notice that taylor attains a greater precision on the coordinates than either the DOPRI8 or the Bulirsch–Stöer.

Investigations on Optimal Design of a U-Tube Steam Generator

2010 ◽  
Author(s):  
Hui-min Qin ◽  
Chang-qi Yan ◽  
Meng Wang ◽  
Shi-jing He
Keyword(s):  
Optimal Design ◽  
Steam Generator ◽  
Optimization Techniques ◽  
Point Of View ◽  
Geometric Constraints ◽  
Optimal Designs ◽  
Optimal Method ◽  
Obvious Effect ◽  
Pressurized Water ◽  
Performance Point

Steam generator is one of the key equipments in the pressurized water reactor, from the performance point of view, it is necessary to apply optimization techniques to the design of the steam generator. In this work, the optimal designs of a U-tube steam generator (UTSG), taking minimization of the total volume and net weight as objective respectively, are carried out by considering thermohydraulic and geometric constraints using a complex-genetic algorithm (CGA). And the sensitivities of some parameters which influence the total volume and net weight of UTSG are also analyzed. Under the condition of constant secondary thermalhydraulic parameters of the steam generator, the optimal design indicates an obvious effect taking either the overall volume or the total weight of the steam generator as the objective. The optimization results show that the proposed optimal method is feasible and effective. And the results of optimal designs and sensitivity analysis would provide guidance in the engineering design of UTSG.

scholarly journals Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields

2019 ◽  
Vol 22 (01) ◽  
pp. 1950001 ◽  
Author(s):  
Boris O. Volkov
Keyword(s):  
Differential Operators ◽  
Equations Of Motion ◽  
Parallel Transport ◽  
System Of Differential Equations ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Dirac Equations ◽  
Lévy Laplacian ◽  
Higgs Fields

We study the Lévy infinite-dimensional differential operators (differential operators defined by the analogy with the Lévy Laplacian) and their relationship to the Yang–Mills equations. We consider the parallel transport on the space of curves as an infinite-dimensional analogue of chiral fields and show that it is a solution to the system of differential equations if and only if the associated connection is a solution to the Yang–Mills equations. This system is an analogue of the equations of motion of chiral fields and contains the Lévy divergence. The systems of infinite-dimensional equations containing Lévy differential operators, that are equivalent to the Yang–Mills–Higgs equations and the Yang–Mills–Dirac equations (the equations of quantum chromodynamics), are obtained. The equivalence of two ways to define Lévy differential operators is shown.

scholarly journals Unified formalism for higher-order variational problems and its applications in optimal control

2014 ◽  
Vol 11 (04) ◽  
pp. 1450034 ◽  
Author(s):  
Leonardo Colombo ◽  
Pedro Daniel Prieto-Martínez
Keyword(s):  
Optimal Control ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Higher Order ◽  
Point Of View ◽  
Regular Case ◽  
Underactuated Mechanical Systems ◽  
Interesting Application ◽  
Principal Bundles ◽  
Order Constraints

In this paper, we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical Skinner–Rusk approach for the case of Lagrangian dynamics with higher-order constraints. We study a regular case where it is possible to establish a symplectic framework and, as a consequence, to obtain a unique vector field determining the dynamics. As an interesting application we deduce the equations of motion for optimal control of underactuated mechanical systems defined on principal bundles.

scholarly journals A COHOMOLOGICAL INTERPRETATION OF THE MIGDAL–MAKEENKO EQUATIONS

2002 ◽  
Vol 17 (08) ◽  
pp. 481-489 ◽  
Author(s):  
A. AGARWAL ◽  
S. G. RAJEEV
Keyword(s):  
Lie Algebra ◽  
Equations Of Motion ◽  
Generating Functional ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Change Of Variables ◽  
Anomalous Term ◽  
Large N ◽  
Infinite Dimensional Lie Algebra ◽  
Cohomological Interpretation

The equations of motion of quantum Yang–Mills theory (in the planar "large-N" limit), when formulated in loop-space are shown to have an anomalous term, which makes them analogous to the equations of motion of WZW models. The anomaly is the Jacobian of the change of variables from the usual ones, i.e. the connection one-form A, to the holonomy U. An infinite-dimensional Lie algebra related to this change of variables (the Lie algebra of loop substitutions) is developed, and the anomaly is interpreted as an element of the first cohomology of this Lie algebra. The Migdal–Makeenko equations are shown to be the condition for the invariance of the Yang–Mills generating functional Z under the action of the generators of this Lie algebra. Connections of this formalism to the collective field approach of Jevicki and Sakita are also discussed.

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