scholarly journals Gauging Newton's law

2007 ◽  
Vol 85 (4) ◽  
pp. 307-344 ◽  
Author(s):  
James T Wheeler
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Measurement Theory ◽  
Hamiltonian Mechanics ◽  
Newtonian Mechanics ◽  
Lagrangian Mechanics ◽  
Newton's Law ◽  
Newton’S Law ◽  
Lagrangian And Hamiltonian Mechanics ◽  
Systematic Development

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton's law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal measurement theory leads to Hamiltonian mechanics. PACS Nos.: 45.20.Jj, 11.25.Hf, 45.10.–b

scholarly journals A SURVEY OF LAGRANGIAN MECHANICS AND CONTROL ON LIE ALGEBROIDS AND GROUPOIDS

2006 ◽  
Vol 03 (03) ◽  
pp. 509-558 ◽  
Author(s):  
JORGE CORTÉS ◽  
MANUEL DE LEÓN ◽  
JUAN C. MARRERO ◽  
D. MARTÍN DE DIEGO ◽  
EDUARDO MARTÍNEZ
Keyword(s):  
Control Systems ◽  
Classical Field Theory ◽  
Nonholonomic Constraints ◽  
Classical Field ◽  
Lie Algebroids ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Geometric Description ◽  
Lagrangian And Hamiltonian Mechanics ◽  
And Control

In this survey, we present a geometric description of Lagrangian and Hamiltonian Mechanics on Lie algebroids. The flexibility of the Lie algebroid formalism allows us to analyze systems subject to nonholonomic constraints, mechanical control systems, Discrete Mechanics and extensions to Classical Field Theory within a single framework. Various examples along the discussion illustrate the soundness of the approach.

scholarly journals On the existence of exotic matter in classical Newtonian mechanics

2019 ◽  
Vol 34 (06) ◽  
pp. 1950049
Author(s):  
Sabbir A. Rahman
Keyword(s):  
Potential Energy ◽  
Total Energy ◽  
Exotic Matter ◽  
Newtonian Mechanics ◽  
Particle Type ◽  
Ordinary Matter ◽  
Newton's Law ◽  
Newton’S Law ◽  
Energy And Momentum ◽  
Rich Spectrum

According to Newton’s law of gravitation, the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter, all three of these are equal and positive. We consider here the more general case where these quantities are equal in magnitude for a given particle but can differ in sign. The resulting set of possible interactions allows each particle type to be assigned to one of precisely four different classes, and the results of N-body simulations show that the corresponding dynamics can give rise to a fairly rich spectrum of possible outcomes, some of which are familiar from nature at various scales. Total energy and momentum are conserved by all of these interactions if the definitions of momentum and kinetic and potential energy are suitably generalized.

Study of Kynematics and Dynamics in the Traffic of Rembangan Tourism in the Jember Regency as Learning Resources for Physics Learning in the Senior High School

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Alfido Fauzy Zakaria ◽  
Bambang Supriadi ◽  
Trapsilo Prihandono
Keyword(s):  
High School ◽  
School Teacher ◽  
High School Teacher ◽  
Senior High School ◽  
Circular Motion ◽  
Rectilinear Motion ◽  
Learning Resources ◽  
Physics Learning ◽  
Newton's Law ◽  
Newton’S Law

One branch of physics is mechanics. Based on interviews to Senior High School teacher in Jember, mechanics is difficult to learn. The eksternals factor this chapter is dificult to learn is learning Resources. The learning Resources are often less contextuall with around the phenomenon of students. The contextuall learning Resources in the Jember Regency is study of kynematics and dynamics in the traffic of Rembangan Tourism. From this experiment, we get data can be used as a learning resources chapter uniform rectilinear motion, decelerated uniform rectilinear motion, accelerated uniform rectilinear motion, Newton’s Law, and circular motion.

Hamiltonian Mechanics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Angular Momentum ◽  
Jacobi Equation ◽  
Modern Theory ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Canonical Transformations ◽  
Canonical Variables ◽  
Light Waves ◽  
Hamilton Jacobi Equation ◽  
Common Action

Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain qualitative answers to a wider ranger of problems than Lagrangian Mechanics. It is explained how Hamilton’s canonical equations arise, why the Hamiltonian is the “central conception of all modern theory” (quote of Schrödinger’s), what the “p − q” variables are, and what phase space is. It is also explained how the famous conservation theorems arise (for energy, linear momentum, and angular momentum), and the connection with symmetry. The Hamilton-Jacobi Equation is derived using infinitesimal canonical transformations (ICTs), and predicts wavefronts of “common action” spreading out in (configuration) space. An analogy can be made with geometrical optics and Huygen’s Principle for the spreading out of light waves. It is shown how Hamilton’s Mechanics can lead into quantum mechanics.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals Non-standard compactifications with mass gaps and Newton's law

1999 ◽  
Vol 1999 (10) ◽  
pp. 013-013 ◽  
Author(s):  
Andreas Brandhuber ◽  
Konstadinos Sfetsos
Keyword(s):  
Newton's Law ◽  
Newton’S Law

scholarly journals META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

2009 ◽  
Vol 24 (27) ◽  
pp. 5051-5120
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
The Other ◽  
Multiple Product

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

scholarly journals HAMILTONIAN COHOMOLOGICAL DERIVATION OF FOUR-DIMENSIONAL NONLINEAR GAUGE THEORIES

2002 ◽  
Vol 17 (16) ◽  
pp. 2191-2210 ◽  
Author(s):  
C. BIZDADEA ◽  
E. M. CIOROIANU ◽  
S. O. SALIU
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Gauge Algebra ◽  
Brst Cohomology ◽  
Nonlinear Gauge

Consistent couplings among a set of scalar fields, two types of one-forms and a system of two-forms are investigated in the light of the Hamiltonian BRST cohomology, giving a four-dimensional nonlinear gauge theory. The emerging interactions deform the first-class constraints, the Hamiltonian gauge algebra, as well as the reducibility relations.

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