SOME COMMENTS ON THE DYNAMICS OF EXTENDED OBJECTS

1998 ◽  
Vol 13 (17) ◽  
pp. 2979-2990 ◽  
Author(s):  
U. KHANAL
Keyword(s):  
Wave Equation ◽  
Energy Density ◽  
Pure Shear ◽  
Equation Of Motion ◽  
Conducting Medium ◽  
Constant Density ◽  
Metric Tensor ◽  
World Volume ◽  
The World ◽  
Hilbert Action

A variational method is used to investigate the dynamics of extended objects. The stationary world volume requires the internal coordinates to propagate as free waves. Stationarity of the action which is the integral of a variable energy density over the world volume leads to the wave equation in a medium, with conductivity given by the gradient of the logarithm of reciprocal energy density, constant density corresponding to free space. The Einstein–Hilbert action for the world curvature gives an equation of motion which, in world space with the Einstein tensor proportional to the metric tensor, reduces to the free wave equation. A similar method applied to the action consisting of the surface area enclosing an incompressible world volume undergoing pure shear again yields the wave equation in a conducting medium. Simultaneous stationarity of the volume can be imposed with a stationary area only in the case of pure shear; stationary Einstein–Hilbert action can also be included and lead to an equation of motion which has a similar interpretation of the wave in the conducting medium. Some Green functions applicable to the medium with constant conductivity are also presented.

FURTHER COMMENTS ON THE DYNAMICS OF EXTENDED OBJECTS

1998 ◽  
Vol 13 (34) ◽  
pp. 2757-2761 ◽  
Author(s):  
U. KHANAL
Keyword(s):  
Wave Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Imaginary Axis ◽  
Momentum Tensor ◽  
Positive Pressure ◽  
Positive Energy ◽  
Constant Density ◽  
Vacuum Interface ◽  
Hilbert Action

The equation of motion of the internal coordinates of a p-brane, arising from the stationarity of the world space Einstein–Hilbert action, is discussed. Assuming the Einstein equation of general relativity, with the energy–momentum tensor of a perfect fluid having positive energy density, it is shown that the governing equation, in matter dominated regions with positive pressure is a (p+1)-dimensional elliptic differential equation which reduces to the (p+1)-dimensional Laplace equation for constant density and pressure. The EOM becomes a hyperbolic p-dimensional wave equation in conducto-dispersive medium only in regions of world space, like those dominated by vacuum, where the total pressure is negative. The Green's function of the matter dominated, elliptic potential problem presented here for p=3, can be analytically continued into the complexified time domain to make contact on the imaginary axis with the Green's function of the wave equation for vacuum domination. Such considerations will allow the study of the matter–vacuum interface using complex time, whence matter domination with positive pressure would be represented on the real axis, vacuum domination with negative pressure on the imaginary axis, and the transition represented by the complex region.

scholarly journals ON TARGET SPACE DUALITY IN p-BRANES

1995 ◽  
Vol 10 (05) ◽  
pp. 441-450 ◽  
Author(s):  
R. PERCACCI ◽  
E. SEZGIN
Keyword(s):  
Dimensional Space ◽  
Target Space ◽  
Field Equations ◽  
Parameter Group ◽  
Duality Transformations ◽  
World Volume ◽  
The World ◽  
Dimensional Space Time ◽  
Background Fields ◽  
Two Parameter

We study the target space duality transformations in p-branes as transformations which mix the world volume field equations with Bianchi identities. We consider an (m+p+1)-dimensional space-time with p+1 dimensions compactified, and a particular form of the background fields. We find that while a GL (2) = SL (2) × R group is realized when m = 0, only a two-parameter group is realized when m > 0.

The Waterfowl of the World. Volume One Jean Delacour

The Auk ◽  
1956 ◽  
Vol 73 (2) ◽  
pp. 298-299
Author(s):  
Robert W. Storer
Keyword(s):  
World Volume ◽  
The World

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

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