30,671 research outputs found
Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
The issue of de Sitter invariance for a massless minimally coupled scalar
field is revisited. Formally, it is possible to construct a de Sitter invariant
state for this case provided that the zero mode of the field is quantized
properly. Here we take the point of view that this state is physically
acceptable, in the sense that physical observables can be computed and have a
reasonable interpretation. In particular, we use this vacuum to derive a new
result: that the squared difference between the field at two points along a
geodesic observer's space-time path grows linearly with the observer's proper
time for a quantum state that does not break de Sitter invariance. Also, we use
the Hadamard formalism to compute the renormalized expectation value of the
energy momentum tensor, both in the O(4) invariant states introduced by Allen
and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum
energy density in the O(4) invariant case is larger than in the de Sitter
invariant case.Comment: TUTP-92-1, to appear in Phys. Rev.
Cosmological attractors in massive gravity
We study Lorentz-violating models of massive gravity which preserve rotations
and are invariant under time-dependent shifts of the spatial coordinates. In
the linear approximation the Newtonian potential in these models has an extra
``confining'' term proportional to the distance from the source. We argue that
during cosmological expansion the Universe may be driven to an attractor point
with larger symmetry which includes particular simultaneous dilatations of time
and space coordinates. The confining term in the potential vanishes as one
approaches the attractor. In the vicinity of the attractor the extra
contribution is present in the Friedmann equation which, in a certain range of
parameters, gives rise to the cosmic acceleration.Comment: 26 pages, 1 figur
Coherent States for 3d Deformed Special Relativity: semi-classical points in a quantum flat spacetime
We analyse the quantum geometry of 3-dimensional deformed special relativity
(DSR) and the notion of spacetime points in such a context, identified with
coherent states that minimize the uncertainty relations among spacetime
coordinates operators. We construct this system of coherent states in both the
Riemannian and Lorentzian case, and study their properties and their geometric
interpretation.Comment: RevTeX4, 20 page
Three dimensional loop quantum gravity: coupling to point particles
We consider the coupling between three dimensional gravity with zero
cosmological constant and massive spinning point particles. First, we study the
classical canonical analysis of the coupled system. Then, we go to the
Hamiltonian quantization generalizing loop quantum gravity techniques. We give
a complete description of the kinematical Hilbert space of the coupled system.
Finally, we define the physical Hilbert space of the system of self-gravitating
massive spinning point particles using Rovelli's generalized projection
operator which can be represented as a sum over spin foam amplitudes. In
addition we provide an explicit expression of the (physical) distance operator
between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde
About Lorentz invariance in a discrete quantum setting
A common misconception is that Lorentz invariance is inconsistent with a
discrete spacetime structure and a minimal length: under Lorentz contraction, a
Planck length ruler would be seen as smaller by a boosted observer. We argue
that in the context of quantum gravity, the distance between two points becomes
an operator and show through a toy model, inspired by Loop Quantum Gravity,
that the notion of a quantum of geometry and of discrete spectra of geometric
operators, is not inconsistent with Lorentz invariance. The main feature of the
model is that a state of definite length for a given observer turns into a
superposition of eigenstates of the length operator when seen by a boosted
observer. More generally, we discuss the issue of actually measuring distances
taking into account the limitations imposed by quantum gravity considerations
and we analyze the notion of distance and the phenomenon of Lorentz contraction
in the framework of ``deformed (or doubly) special relativity'' (DSR), which
tentatively provides an effective description of quantum gravity around a flat
background. In order to do this we study the Hilbert space structure of DSR,
and study various quantum geometric operators acting on it and analyze their
spectral properties. We also discuss the notion of spacetime point in DSR in
terms of coherent states. We show how the way Lorentz invariance is preserved
in this context is analogous to that in the toy model.Comment: 25 pages, RevTe
The space of essential matrices as a Riemannian quotient manifold
The essential matrix, which encodes the epipolar constraint between points in two projective views,
is a cornerstone of modern computer vision. Previous works have proposed different characterizations
of the space of essential matrices as a Riemannian manifold. However, they either do not consider the
symmetric role played by the two views, or do not fully take into account the geometric peculiarities
of the epipolar constraint. We address these limitations with a characterization as a quotient manifold
which can be easily interpreted in terms of camera poses. While our main focus in on theoretical
aspects, we include applications to optimization problems in computer vision.This work was supported by grants NSF-IIP-0742304, NSF-OIA-1028009, ARL MAST-CTA W911NF-08-2-0004, and ARL RCTA W911NF-10-2-0016, NSF-DGE-0966142, and NSF-IIS-1317788
The Residual Mass Term in the Heavy Quark Effective Theory
We reformulate the heavy quark effective theory in the presence of a residual
mass term, which has been taken to vanish in previous analyses. While such a
convention is permitted, the inclusion of a residual mass allows us to resolve
a potential ambiguity in the choice of the expansion parameter which defines
the effective theory. We show to subleading order in the mass expansion that
physical quantities computed in the effective theory do not depend on the
expansion parameter.Comment: 14 page
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