scholarly journals DUALITY IN EQUATIONS OF MOTION FROM SPACE–TIME DEPENDENT LAGRANGIANS

2000 ◽  
Vol 15 (14) ◽  
pp. 901-911 ◽  
Author(s):  
RAJSEKHAR BHATTACHARYYA ◽  
DEBASHIS GANGOPADHYAY
Keyword(s):  
Equations Of Motion ◽  
Space Time ◽  
Quantization Condition ◽  
Time Dependent ◽  
Classical Solutions ◽  
String Solution ◽  
Yang Mills ◽  
Dirac Quantization ◽  
Lagrangian Field Theory ◽  
Condition C

Starting from Lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit space–time dependence of the Lagrangian. Poincaré invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both Abelian and non-Abelian dualities. We illustrate how (a) Dirac string solution, (b) Dirac quantization condition, (c) 't Hooft–Polyakov monopole solutions and (d) a procedure emerges for obtaining new classical solutions of Yang–Mills (YM) theory. Moreover, these results occur in a way that is strongly reminiscent of the holographic principle.

OBSERVATIONS ON A U(1) × U(1) VECTOR THEORY

2002 ◽  
Vol 17 (16) ◽  
pp. 2211-2217
Author(s):  
D. G. C. MCKEON
Keyword(s):  
Vector Fields ◽  
Equations Of Motion ◽  
Quantization Condition ◽  
Constraint Condition ◽  
Supersymmetric Version ◽  
Dirac Quantization ◽  
Covariant Gauge ◽  
Vector Theory ◽  
Two Sectors ◽  
Conserved Currents

The symmetry between two sectors of a model containing two U(1) vector fields (related by a constraint condition) and two conserved currents is examined. The equations of motion for the vector fields, once the constraint condition is applied, is similar in form to the Maxwell equations in the presence of both electric and magnetic charge. The Dirac quantization condition need not be applied. The propagators for the vector fields are computed in a covariant gauge, demonstrating that the model is unitary and renormalizable. A supersymmetric version of the model is presented.

Higher spin theories in flat space–time

2018 ◽  
Vol 33 (34) ◽  
pp. 1845007
Author(s):  
Loriano Bonora
Keyword(s):  
Equations Of Motion ◽  
Flat Space ◽  
Space Time ◽  
Local Fields ◽  
Field Theories ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Spin ◽  
Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

scholarly journals Dirac quantization condition for monopole in noncommutative space-time

2009 ◽  
Vol 79 (12) ◽  
Author(s):  
Masud Chaichian ◽  
Subir Ghosh ◽  
Miklos Långvik ◽  
Anca Tureanu
Keyword(s):  
Space Time ◽  
Quantization Condition ◽  
Noncommutative Space ◽  
Dirac Quantization

CHAOS IN ABELIAN AND NON-ABELIAN HIGGS SYSTEMS

1993 ◽  
Vol 08 (10) ◽  
pp. 1755-1772 ◽  
Author(s):  
B. DEY ◽  
C.N. KUMAR ◽  
A. SEN
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Higgs Model ◽  
Time Dependent ◽  
Abelian Higgs Model ◽  
Surface Of Section ◽  
Yang Mills ◽  
Poincaré Surface Of Section ◽  
Chaotic Nature ◽  
Parameter Values

The nonintegrability and chaotic nature of the Yang-Mills Higgs systems are considered. We have studied the Abelian Higgs model and the SO(3) Georgi-Glashow model (non-Abelian Higgs model), which possess vortices and monopole solutions respectively. The Painlevé analysis of the corresponding time-dependent equations of motion shows that both systems are nonintegrable for all choices of the parameter values. The Poincare surface-of-section plot shows the presence of chaotic trajectories in the phase space at certain parameter values for both systems. The chaotic nature of the trajectories is also indicated by the computations of the Lyapunov exponents of the corresponding systems.

scholarly journals BRANE SOLUTIONS IN TIME-DEPENDENT BACKGROUNDS IN D = 11 SUPERGRAVITY AND IN TYPE II STRING THEORIES

2008 ◽  
Vol 23 (16n17) ◽  
pp. 2525-2540 ◽  
Author(s):  
SRIKUMAR SEN GUPTA
Keyword(s):  
String Theory ◽  
Equations Of Motion ◽  
Space Time ◽  
Time Dependent ◽  
Type Ii ◽  
Reduced Equations ◽  
Special Cases ◽  
M Theory ◽  
String Theories

We obtain explicit time-dependent brane solutions in M-theory as well as in string theory by solving the reduced equations of motion (which follow, as in Int. J. Mod. Phys. A17, 4647 (2002), from 11-dimensional supergravity) for a class of brane solutions in curved backgrounds. The behavior of our solutions in both asymptotic and near-horizon limits are studied. It is shown that our time-dependent solutions serve as explicit examples of branes in singular, cosmological backgrounds. In some special cases the asymptotic and the boundary AdS solutions can be identified as Milne × Rn space–time.

scholarly journals MANIFESTLY O(d,d) INVARIANT APPROACH TO SPACE-TIME DEPENDENT STRING VACUA

1991 ◽  
Vol 06 (37) ◽  
pp. 3397-3404 ◽  
Author(s):  
K. A. MEISSNER ◽  
G. VENEZIANO
Keyword(s):  
Black Hole ◽  
Renormalization Group ◽  
General Solution ◽  
Equations Of Motion ◽  
Space Time ◽  
Low Energy ◽  
Time Dependent ◽  
Energy Equations ◽  
Invariant Approach ◽  
Black Hole Solutions

An O(d,d) symmetry of the manifold of string vacua that do not depend on d (out of D) space-time coordinates has been recently identified. Here we write down, for d=D-1, the low energy equations of motion and their general solution in a manifestly O(d,d)-invariant form, pointing out an amusing similarity with the renormalization group framework. Previously considered cosmological and black hole solutions are reproduced as particular examples.

scholarly journals A brief review of E theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1630043 ◽  
Author(s):  
Peter West
Keyword(s):  
Infinite Number ◽  
Equations Of Motion ◽  
Space Time ◽  
Unified Theory ◽  
Dynamical Equations ◽  
Supergravity Theory ◽  
Maximal Supergravity ◽  
Abdus Salam ◽  
Strings And Branes ◽  
Time Lead

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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