20,981 research outputs found
Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
We derive a collective field theory of the singlet sector of the Sp(2N) sigma
model. Interestingly the hamiltonian for the bilocal collective field is the
same as that of the O(N) model. However, the large-N saddle points of the two
models differ by a sign. This leads to a fluctuation hamiltonian with a
negative quadratic term and alternating signs in the nonlinear terms which
correctly reproduces the correlation functions of the singlet sector. Assuming
the validity of the connection between O(N) collective fields and higher spin
fields in AdS, we argue that a natural interpretation of this theory is by a
double analytic continuation, leading to the dS/CFT correspondence proposed by
Anninos, Hartman and Strominger. The bi-local construction gives a map into the
bulk of de Sitter space-time. Its geometric pseudospin-representation provides
a framework for quantization and definition of the Hilbert space. We argue that
this is consistent with finite N grassmanian constraints, establishing the
bi-local representation as a nonperturbative framework for quantization of
Higher Spin Gravity in de Sitter space.Comment: 1 figur
Geometric Quantization and Two Dimensional QCD
In this article, we will discuss geometric quantization of 2d QCD with
fermionic and bosonic matter fields. We identify the respective large-N_c phase
spaces as the infinite dimensional Grassmannian and the infinite dimensional
Disc. The Hamiltonians are quadratic functions, and the resulting equations of
motion for these classical systems are nonlinear. In a previous publication,
the first author has shown that the linearization of the equations of motion
for the Grassmannian gave the `t Hooft equation. We will see that the
linearization in the bosonic case leads to the scalar analog of the `t Hooft
equation found by Tomaras.Comment: 46 pages, Latex, no figure
Conditional hitting time estimation in a nonlinear filtering model by the Brownian bridge method
The model consists of a signal process which is a general Brownian
diffusion process and an observation process , also a diffusion process,
which is supposed to be correlated to the signal process. We suppose that the
process is observed from time 0 to at discrete times and aim to
estimate, conditionally on these observations, the probability that the
non-observed process crosses a fixed barrier after a given time . We
formulate this problem as a usual nonlinear filtering problem and use optimal
quantization and Monte Carlo simulations techniques to estimate the involved
quantities
Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field
We investigate analytically and numerically the dynamics of domain walls in a
spin chain with ferromagnetic Ising interaction and subject to an external
magnetic field perpendicular to the easy magnetization axis (transverse field
Ising model). The analytical results obtained within the continuum
approximation and numerical simulations performed for discrete classical model
are used to analyze the quantum properties of domain walls using the
semiclassical approximation. We show that the domain wall spectrum shows a band
structure consisting of 2 non-intersecting zones.Comment: 15 pages, 9 figure
- …