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Correspondence between Minkowski and de Sitter Quantum Field Theory
In this letter we show that the ``preferred'' Klein-Gordon Quantum Field
Theories (QFT's) on a d-dimensional de Sitter spacetime can be obtained from a
Klein-Gordon QFT on a (d+1)-dimensional ``ambient'' Minkowski spacetime
satisfying the spectral condition and, conversely, that a Klein-Gordon QFT on a
(d+1)-dimensional ``ambient'' Minkowski spacetime satisfying the spectral
condition can be obtained as superposition of d-dimensional de Sitter
Klein-Gordon fields in the preferred vacuum. These results establish a
correspondence between QFT's living on manifolds having different dimensions.
The method exposed here can be applied to study other situations and notably
QFT on Anti de Sitter spacetime.Comment: 7 pages, no figures, typos corrected, added one referenc
On amplitude zeros at threshold
The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories
is studied. We find a differential equation for the scalar potential, which
incorporates all known cases where the 2 to n amplitudes at threshold vanish
for all sufficiently large , in all space-time dimensions, . This
equation is related to the reflectionless potentials of Quantum Mechanics and
to integrable theories in 1+1 dimensions. As an application, we find that the
sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential,
also have amplitude zeros at threshold, , for and
, independently of the mass and the coupling constant.Comment: 6 pages, Latex, CERN-TH.6762/9
M Theory from World-Sheet Defects in Liouville String
We have argued previously that black holes may be represented in a D-brane
approach by monopole and vortex defects in a sine-Gordon field theory model of
Liouville dynamics on the world sheet. Supersymmetrizing this sine-Gordon
system, we find critical behaviour in 11 dimensions, due to defect condensation
that is the world-sheet analogue of D-brane condensation around an extra
space-time dimension in M theory. This supersymmetric description of Liouville
dynamics has a natural embedding within a 12-dimensional framework suggestive
of F theory.Comment: 17 pages LATEX, 1 epsf figure include
Relativistic Comparison Theorems
Comparison theorems are established for the Dirac and Klein--Gordon
equations. We suppose that V^{(1)}(r) and V^{(2)}(r) are two real attractive
central potentials in d dimensions that support discrete Dirac eigenvalues
E^{(1)}_{k_d\nu} and E^{(2)}_{k_d\nu}. We prove that if V^{(1)}(r) \leq
V^{(2)}(r), then each of the corresponding discrete eigenvalue pairs is ordered
E^{(1)}_{k_d\nu} \leq E^{(2)}_{k_d\nu}. This result generalizes an earlier more
restrictive theorem that required the wave functions to be node free. For the
the Klein--Gordon equation, similar reasoning also leads to a comparison
theorem provided in this case that the potentials are negative and the
eigenvalues are positive.Comment: 6 page
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
Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?
We discuss Coleman's theorem concerning the energy density of the ground
state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975).
According to this theorem the energy density of the ground state of the
sine-Gordon model should be unbounded from below for coupling constants beta^2
> 8 pi. The consequence of this theorem would be the non-existence of the
quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that
the energy density of the ground state in the sine-Gordon model is bounded from
below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's
theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and
soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version
accepted for publication in Journal of Physics
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