scholarly journals Electrically charged localized structures

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
D. Bazeia ◽  
M. A. Marques ◽  
R. Menezes
Keyword(s):  
Gauge Field ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Scalar Fields ◽  
Abelian Gauge ◽  
First Order ◽  
Localized Structures ◽  
Spatial Dimensions ◽  
Electrically Charged ◽  
First Order Differential Equations

AbstractThis work deals with an Abelian gauge field in the presence of an electric charge immersed in a medium controlled by neutral scalar fields, which interact with the gauge field through a generalized dielectric function. We develop an interesting procedure to solve the equations of motion, which is based on the minimization of the energy, leading us to a first order framework where minimum energy solutions of first order differential equations solve the equations of motion. We investigate two distinct models in two and three spatial dimensions and illustrate the general results with some examples of current interest, implementing a simple way to solve the problem with analytical solutions that engender internal structure.

TOPOLOGICAL DEFECTS AND THE TRIAL ORBIT METHOD

2002 ◽  
Vol 17 (29) ◽  
pp. 1945-1953 ◽  
Author(s):  
D. BAZEIA ◽  
W. FREIRE ◽  
L. LOSANO ◽  
R. F. RIBEIRO
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Topological Defects ◽  
Scalar Fields ◽  
Explicit Solutions ◽  
Orbit Method ◽  
First Order ◽  
Real Scalar ◽  
Second Order Equations ◽  
First Order Differential Equations

We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects and search for explicit defect solutions using the trial orbit method. As we know, under certain circumstances the second-order equations of motion can be solved by solutions of first-order differential equations. In this case we show that the trial orbit method can be used very efficiently to obtain explicit solutions.

scholarly journals GLOBAL DEFECTS IN FIELD THEORY WITH APPLICATIONS TO CONDENSED MATTER

2005 ◽  
Vol 19 (17) ◽  
pp. 801-819 ◽  
Author(s):  
D. BAZEIA ◽  
J. MENEZES ◽  
R. MENEZES
Keyword(s):  
Field Theory ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Scalar Fields ◽  
Higher Dimensions ◽  
Spatial Dimension ◽  
Specific Form ◽  
First Order ◽  
Real Scalar ◽  
First Order Differential Equations

We review investigations on defects in systems described by real scalar fields in (D, 1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D = 1. We illustrate the procedure examining specific models and showing how they may be used in applications in different contexts in condensed matter physics, and in other areas.

scholarly journals Conserved Currents in Supersymmetric Quantum Cosmology?

1997 ◽  
Vol 06 (05) ◽  
pp. 625-641 ◽  
Author(s):  
P. V. Moniz
Keyword(s):  
Differential Equations ◽  
Quantum Cosmology ◽  
Scalar Fields ◽  
Square Root ◽  
Root Structure ◽  
Complex Scalar ◽  
First Order ◽  
Class A ◽  
Conserved Currents ◽  
First Order Differential Equations

In this paper we investigate whether conserved currents can be sensibly defined in super-symmetric minisuperspaces. Our analysis deals with k = +1 FRW and Bianchi class-A models. Supermatter in the form of scalar supermultiplets is included in the former. Moreover, we restrict ourselves to the first-order differential equations derived from the Lorentz and supersymmetry constraints. The "square-root" structure of N = 1 super-gravity was our motivation to contemplate this interesting research. We show that conserved currents cannot be adequately established except for some very simple scenarios. Otherwise, equations of the type ∇a Ja = 0 may only be obtained from Wheeler–DeWittlike equations, which are derived from the supersymmetric algebra of constraints. Two appendices are included. In Appendix A we describe some interesting features of quantum FRW cosmologies with complex scalar fields when supersymmetry is present. In particular, we explain how the Hartle–Hawking state can now be satisfactorily identified. In Appendix B we initiate a discussion about the retrieval of classical properties from supersymmetric quantum cosmologies.

scholarly journals Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Roberto Tanzi ◽  
Domenico Giulini
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Hamiltonian Formulation ◽  
Scalar Fields ◽  
Higgs Model ◽  
Massless Scalar ◽  
Asymptotic Symmetry ◽  
Abelian Gauge ◽  
Abelian Higgs Model ◽  
Asymptotic Symmetries

Abstract We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

Equations of motion with the identity mass matrix for holonomic systems

2004 ◽  
Vol 218 (7) ◽  
pp. 731-736
Author(s):  
P Herman
Keyword(s):  
Differential Equations ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Dynamical Equations ◽  
First Order ◽  
Interesting Insight ◽  
Holonomic Systems ◽  
Insight Into ◽  
First Order Differential Equations

Some consequences concerning holonomic systems described in terms of the inertial quasi-velocities (IQV) are discussed in this note. Introducing the IQV vector into Lagrange's formulation leads to first-order equations with the identity mass matrix of the system. The first-order differential equations give an interesting insight into dynamics and some important properties. The two examples that are provided use the dynamical equations in terms of IQV.

Hamiltonian mechanics

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Configuration Space ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Hamiltonian Mechanics ◽  
Lagrange Equations ◽  
First Order ◽  
Point Transformations ◽  
First Order Differential Equations

This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension of the phase space is double that of the configuration space, so that in addition to point transformations, it is possible to perform more general transformations in order to simplify solving the equations of motion.

scholarly journals Yang-Mills lattice on CUDA

2013 ◽  
Vol 5 (2) ◽  
pp. 184-211 ◽  
Author(s):  
Richárd Forster ◽  
Ágnes Fülöp
Keyword(s):  
Gauge Field ◽  
Equations Of Motion ◽  
Field Tensor ◽  
Classical Lattice ◽  
Regular Lattice ◽  
Abelian Gauge ◽  
Yang Mills ◽  
3 Dimensional ◽  
Classical Fields ◽  
Physical Quantities

Abstract The Yang-Mills fields have an important role in the non- Abelian gauge field theory which describes the properties of the quarkgluon plasma. The real time evolution of the classical fields is given by the equations of motion which are derived from the Hamiltonians to contain the term of the SU(2) gauge field tensor. The dynamics of the classical lattice Yang-Mills equations are studied on a 3 dimensional regular lattice. During the solution of this system we keep the total energy on constant values and it satisfies the Gauss law. The physical quantities are desired to be calculated in the thermodynamic limit. The broadly available computers can handle only a small amount of values, while the GPUs provide enough performance to reach out for higher volumes of lattice vertices which approximates the aforementioned limit.

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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