146 research outputs found
Quantization of a Scalar Field in Two Poincar\'e Patches of Anti-de Sitter Space and AdS/CFT
Two sets of modes of a massive free scalar field are quantized in a pair of
Poincar\'e patches of Lorentzian anti-de Sitter (AdS) space, AdS (). It is shown that in Poincar\'e coordinates , the two
boundaries at are connected. When the scalar mass satisfies
a condition , there exist two sets of mode
solutions to Klein-Gordon equation, with distinct fall-off behaviors at the
boundary. By using the fact that the boundaries at are
connected, a conserved Klein-Gordon norm can be defined for these two sets of
scalar modes, and these modes are canonically quantized. Energy is also
conserved. A prescription within the approximation of semi-classical gravity is
presented for computing two- and three-point functions of the operators in the
boundary CFT, which correspond to the two fall-off behaviours of scalar field
solutions.Comment: 35 pages, 8 figures; ver.2: Fig.5, fig. 6 and subsection 2.4
modified; ver.3: Abstract and subsection 2.4 changed. Two figures removed and
one figure added. 33 page
The Hamilton-Jacobi Equations for Strings and p-Branes
Simple derivation of the Hamilton-Jacobi equation for bosonic strings and
p-branes is given. The motion of classical strings and p-branes is described by
two and p+1 local fields, respectively. A variety of local field equations
which reduce to the Hamilton-Jacobi equation in the classical limit are given.
They are essentially nonlinear, having no linear term.Comment: 7 page
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