2,729 research outputs found
Interacting dark energy in gravity
The field equations in gravity derived from the Palatini variational
principle and formulated in the Einstein conformal frame yield a cosmological
term which varies with time. Moreover, they break the conservation of the
energy--momentum tensor for matter, generating the interaction between matter
and dark energy. Unlike phenomenological models of interacting dark energy,
gravity derives such an interaction from a covariant Lagrangian which is
a function of a relativistically invariant quantity (the curvature scalar ).
We derive the expressions for the quantities describing this interaction in
terms of an arbitrary function , and examine how the simplest
phenomenological models of a variable cosmological constant are related to
gravity. Particularly, we show that for a flat,
homogeneous and isotropic, pressureless universe. For the Lagrangian of form
, which is the simplest way of introducing current cosmic acceleration
in gravity, the predicted matter--dark energy interaction rate changes
significantly in time, and its current value is relatively weak (on the order
of 1% of ), in agreement with astronomical observations.Comment: 8 pages; published versio
Restoring Time Dependence into Quantum Cosmology
Mini superspace cosmology treats the scale factor , the lapse function
, and an optional dilation field as canonical variables. While
pre-fixing means losing the Hamiltonian constraint, pre-fixing is
serendipitously harmless at this level. This suggests an alternative to the
Hartle-Hawking approach, where the pre-fixed and its derivatives are
treated as explicit functions of time, leaving and a now mandatory
to serve as canonical variables. The naive gauge pre-fix
is clearly forbidden, causing evolution to freeze altogether, so pre-fixing the
scale factor, say , necessarily introduces explicit time dependence
into the Lagrangian. Invoking Dirac's prescription for dealing with
constraints, we construct the corresponding mini superspace time dependent
total Hamiltonian, and calculate the Dirac brackets, characterized by
, which are promoted to commutation relations in the
quantum theory.Comment: Honorable Mentioned essay - Gravity Research Foundation 201
Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator
As a model, the Pais-Uhlenbeck fourth order oscillator with equation of
motion
is a quantum-mechanical prototype of a field theory containing both second and
fourth order derivative terms. With its dynamical degrees of freedom obeying
constraints due to the presence of higher order time derivatives, the model
cannot be quantized canonically. We thus quantize it using the method of Dirac
constraints to construct the correct quantum-mechanical Hamiltonian for the
system, and find that the Hamiltonian diagonalizes in the positive and negative
norm states that are characteristic of higher derivative field theories.
However, we also find that the oscillator commutation relations become singular
in the limit, a limit which corresponds to a prototype
of a pure fourth order theory. Thus the particle content of the theory cannot be inferred from that of the
theory; and in fact in the limit we find that all of
the negative norm states move off shell, with the
spectrum of asymptotic in and out states of the equal frequency theory being
found to be completely devoid of states with either negative energy or negative
norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero
energy theorem of Boulware, Horowitz and Strominger, and show how in the equal
frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive
energy theorem instead.Comment: RevTeX4, 20 pages. Final version, to appear in Phys. Rev.
On the Implementation of Constraints through Projection Operators
Quantum constraints of the type Q \psi = 0 can be straightforwardly
implemented in cases where Q is a self-adjoint operator for which zero is an
eigenvalue. In that case, the physical Hilbert space is obtained by projecting
onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however,
nontrivial to identify and project onto H_phys when zero is not in the point
spectrum but instead is in the continuous spectrum of Q, because in this case
the kernel of Q is empty.
Here, we observe that the topology of the underlying Hilbert space can be
harmlessly modified in the direction perpendicular to the constraint surface in
such a way that Q becomes non-self-adjoint. This procedure then allows us to
conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on
which one can project as usual. In the simplest case, the necessary change of
topology amounts to passing from an L^2 Hilbert space to a Sobolev space.Comment: 22 pages, LaTe
On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions
It is shown that the well-known triviality of the Einstein field equations in
two dimensions is not a sufficient condition for the Einstein-Hilbert action to
be a total divergence, if the general covariance is to be preserved, that is, a
coordinate system is not fixed. Consequently, a Hamiltonian formulation is
possible without any modification of the two dimensional Einstein-Hilbert
action. We find the resulting constraints and the corresponding gauge
transfromations of the metric tensor.Comment: 9 page
Very Light Cosmological Scalar Fields from a Tiny Cosmological Constant
We discuss a mechanism which generates a mass term for a scalar field in an
expanding universe. The mass of this field turns out to be generated by the
cosmological constant and can be naturally small if protected by a conformal
symmetry which is however broken in the gravitational sector. The mass is
comparable today to the Hubble time. This scalar field could thus impact our
universe today and for example be at the origin of a time variation of the
couplings and masses of the parameters of the standard model.Comment: 11 page
Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background
The effective potential for a dynamical Wick field (dynamical signature)
induced by the quantum effects of massive fields on a topologically non-trivial
dimensional background is considered. It is shown that when the radius of
the compactified dimension is very small compared with (where
is a proper-time cutoff), a flat metric with Lorentzian signature is
preferred on . When the compactification radius
becomes larger a careful analysis of the 1-loop effective potential indicates
that a Lorentzian signature is preferred in both and and that these
results are relatively stable under metrical perturbations
Strongly coupled plasma with electric and magnetic charges
A number of theoretical and lattice results lead us to believe that
Quark-Gluon Plasma not too far from contains not only electrically
charged quasiparticles -- quarks and gluons -- but magnetically charged ones --
monopoles and dyons -- as well. Although binary systems like charge-monopole
and charge-dyon were considered in details before in both classical and quantum
settings, it is the first study of coexisting electric and magnetic particles
in many-body context. We perform Molecular Dynamics study of strongly coupled
plasmas with particles and different fraction of magnetic charges.
Correlation functions and Kubo formulae lead to such transport properties as
diffusion constant, shear viscosity and electric conductivity: we compare the
first two with empirical data from RHIC experiments as well as results from
AdS/CFT correspondence. We also study a number of collective excitations in
these systems.Comment: 2nd version, 22 pages, 32 figures: two important new figures have
been included to compare our results with RHIC experiments and AdS/CFT
results; a few new references and comments are added as wel
Common Space of Spin and Spacetime
Given Lorentz invariance in Minkowski spacetime, we investigate a common
space of spin and spacetime. To obtain a finite spinor representation of the
non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an
indefinite inner product space (IIPS) with a normalized positive probability.
In this IIPS, the common momentum and common variable of a massive fermion turn
out to be ``doubly strict plus-operators''. Due to this nice property, it is
straightforward to show an uncertainty relation between fermion mass and proper
time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,
and the fermion field equations are derivable from the Lagrangians. Finally,
the nonlinear QED equations and Lagrangians are presented as an example.Comment: 17 pages, a reference corrected, final version published on
Foundations of Physics Letters in June of 2005, as a personal tribute to
Einstein and Dira
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