scholarly journals Multi-component scalar fields and the complete factorization of its equations of motion

2019 ◽  
Vol 126 (6) ◽  
pp. 61001 ◽  
Author(s):  
Diego R. Granado
Keyword(s):  
Equations Of Motion ◽  
Scalar Fields ◽  
Complete Factorization

scholarly journals A General Method for Transforming Nonphysical Configurations in BPS States

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
J. R. L. Santos ◽  
A. de Souza Dutra ◽  
O. C. Winter ◽  
R. A. C. Correa
Keyword(s):  
Scalar Field ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Cosmological Parameters ◽  
Topological Defects ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Bps States ◽  
General Method

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model. In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named nonphysical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.

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 Complete factorization of equations of motion for generalized scalar field theories

2017 ◽  
Vol 119 (6) ◽  
pp. 61002 ◽  
Author(s):  
D. Bazeia ◽  
Diego R. Granado ◽  
Elisama E. M. Lima
Keyword(s):  
Scalar Field ◽  
Equations Of Motion ◽  
Field Theories ◽  
Complete Factorization

scholarly journals PALATINI FORMULATION OF MODIFIED GRAVITY WITH A NON-MINIMAL CURVATURE-MATTER COUPLING

2011 ◽  
Vol 26 (20) ◽  
pp. 1467-1480 ◽  
Author(s):  
TIBERIU HARKO ◽  
TOMI S. KOIVISTO ◽  
FRANCISCO S. N. LOBO
Keyword(s):  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Scalar Fields ◽  
Momentum Tensor ◽  
Nonlinear Dependence ◽  
Modified Theories Of Gravity ◽  
Field Equations ◽  
Test Particles ◽  
Theories Of Gravity ◽  
Minimal Curvature

We derive the field equations and the equations of motion for scalar fields and massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi–Cività connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the nonconservation of the energy–momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity. It is pointed out here that the force is of a different nature than in the metric formalism. We also consider the implications of a nonlinear dependence of the action upon the matter Lagrangian.

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.

Classical Electromagnetism

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Equations Of Motion ◽  
Classical Mechanics ◽  
Classical Field Theory ◽  
Scalar Fields ◽  
Local Symmetry ◽  
Momentum Tensor ◽  
Global Symmetry ◽  
Complex Scalar ◽  
Symmetry Properties ◽  
Time Variations

In this chapter, Noether’s theorem as a classical field theory is presented and the properties of variations are again discussed for fields (i.e. field variations, space variations, time variations, spacetime variations), resulting in the Noether condition. Quasisymmetries and spontaneous symmetry breaking are discussed, as well as local symmetry and global symmetry. Following these definitions, Noether’s first theorem and Noether’s second theorem are developed. The classical Schrödinger field is investigated and the key equations of classical mechanics are summarised into a single Lagrangian. Symmetry properties of the field action and equations of motion are then compared. The chapter discusses the energy–momentum tensor, the Klein–Utiyama theorem, the Liouville equation and the Hamilton–Jacobi equation. It also discusses material science, special orthogonal groups and complex scalar fields.

scholarly journals DYNAMICS OF MASSIVE SCALAR FIELDS IN dS SPACE AND THE dS/CFT CORRESPONDENCE

2002 ◽  
Vol 17 (30) ◽  
pp. 4591-4600 ◽  
Author(s):  
ZHE CHANG ◽  
CHENG-BO GUAN
Keyword(s):  
Equations Of Motion ◽  
Scalar Fields ◽  
Wave Functions ◽  
Massive Scalar ◽  
Geometric Properties ◽  
Solutions Of Equations

Global geometric properties of dS space are presented explicitly in various coordinates. A Robertson–Walker-like metric is deduced, which is convenient to be used in the study of dynamics in dS space. Singularities of wave functions of massive scalar fields at boundary are demonstrated. A bulk-boundary propagator is constructed by making use of the solutions of equations of motion. The dS/CFT correspondence and the Strominger mass bound is shown.

scholarly journals Complete factorization of equations of motion in Wess–Zumino theory

2001 ◽  
Vol 521 (3-4) ◽  
pp. 418-420 ◽  
Author(s):  
D Bazeia ◽  
J Menezes ◽  
M.M Santos
Keyword(s):  
Equations Of Motion ◽  
Complete Factorization
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