211 research outputs found
Minimal Ten-parameter Hermitian Texture Zeroes Mass Matrices and the CKM Matrix
Hermitian mass matrices for the up and down quarks with texture zeroes but
with the minimum number of parameters, ten, are investigated. We show how these
{\em minimum parameter} forms can be obtained from a general set of hermitian
matrices through weak basis transformations. For the most simple forms we show
that one can derive exact and compact parametrizations of the CKM mixing matrix
in terms of the elements of these mass matrices (and the quark masses).Comment: 14 pages.Talk given by M.B. at the MRST 98, ``Towards the Theory of
Everything", Montr\'eal, 13-15 May 199
Not all adiabatic vacua are physical states
Adiabatic vacua are known to be Hadamard states. We show, however that the
energy-momentum tensor of a linear Klein-Gordon field on Robertson-Walker
spaces developes a generic singularity on the initial hypersurface if the
adiabatic vacuum is of order less than four. Therefore, adiabatic vacua are
physically reasonable only if their order is at least four.
A certain non-local large momentum expansion of the mode functions has
recently been suggested to yield the subtraction terms needed to remove the
ultraviolet divergences in the energy-momentum tensor. We find that this scheme
fails to reproduce the trace anomaly and therefore is not equivalent to
adiabatic regularisation.Comment: 13 pages, LaTex2
Out-of-equilibrium evolution of scalar fields in FRW cosmology: renormalization and numerical simulations
We present a renormalized computational framework for the evolution of a
self-interacting scalar field (inflaton) and its quantum fluctuations in an FRW
background geometry. We include a coupling of the field to the Ricci scalar
with a general coupling parameter . We take into account the classical and
quantum back reactions, i.e., we consider the the dynamical evolution of the
cosmic scale factor. We perform, in the one-loop and in the large-N
approximation, the renormalization of the equation of motion for the inflaton
field, and of its energy momentum tensor. Our formalism is based on a
perturbative expansion for the mode functions, and uses dimensional
regularization. The renormalization procedure is manifestly covariant and the
counter terms are independent of the initial state. Some shortcomings in the
renormalization of the energy-momentum tensor in an earlier publication are
corrected. We avoid the occurence of initial singularities by constructing a
suitable class of initial states. The formalism is implemented numerically and
we present some results for the evolution in the post-inflationary preheating
era.Comment: 44 pages, uses latexsym, 6 pages with 11 figures in a .ps fil
Attractor states and infrared scaling in de Sitter space
The renormalized expectation value of the energy-momentum tensor for a scalar
field with any mass m and curvature coupling xi is studied for an arbitrary
homogeneous and isotropic physical initial state in de Sitter spacetime. We
prove quite generally that has a fixed point attractor behavior at
late times, which depends only on m and xi, for any fourth order adiabatic
state that is infrared finite. Specifically, when m^2 + xi R > 0,
approaches the Bunch-Davies de Sitter invariant value at late times,
independently of the initial state. When m = xi = 0, it approaches instead the
de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that
this state independent asymptotic value of the energy-momentum tensor is
proportional to the conserved geometrical tensor (3)H_{ab}, which is related to
the behavior of the quantum effective action of the scalar field under global
Weyl rescaling. This relationship serves to generalize the definition of the
trace anomaly in the infrared for massless, non-conformal fields. In the case
m^2 + xi R = 0, but m and xi separately different from zero, grows
linearly with cosmic time at late times. For most values of m and xi in the
tachyonic cases, m^2 + xi R grows exponentially at late cosmic
times for all physically admissable initial states.Comment: 30 pages, 6 figures, 46 kB tar.gz fil
Energy-Momentum Tensor of Particles Created in an Expanding Universe
We present a general formulation of the time-dependent initial value problem
for a quantum scalar field of arbitrary mass and curvature coupling in a FRW
cosmological model. We introduce an adiabatic number basis which has the virtue
that the divergent parts of the quantum expectation value of the
energy-momentum tensor are isolated in the vacuum piece of , and
may be removed using adiabatic subtraction. The resulting renormalized
is conserved, independent of the cutoff, and has a physically transparent,
quasiclassical form in terms of the average number of created adiabatic
`particles'. By analyzing the evolution of the adiabatic particle number in de
Sitter spacetime we exhibit the time structure of the particle creation
process, which can be understood in terms of the time at which different
momentum scales enter the horizon. A numerical scheme to compute as a
function of time with arbitrary adiabatic initial states (not necessarily de
Sitter invariant) is described. For minimally coupled, massless fields, at late
times the renormalized goes asymptotically to the de Sitter invariant
state previously found by Allen and Folacci, and not to the zero mass limit of
the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ
from zero, but satisfy m^2+xi R=0, the energy density and pressure of the
scalar field grow linearly in cosmic time demonstrating that, at least in this
case, backreaction effects become significant and cannot be neglected in de
Sitter spacetime.Comment: 28 pages, Revtex, 11 embedded .ps figure
A formally verified compiler back-end
This article describes the development and formal verification (proof of
semantic preservation) of a compiler back-end from Cminor (a simple imperative
intermediate language) to PowerPC assembly code, using the Coq proof assistant
both for programming the compiler and for proving its correctness. Such a
verified compiler is useful in the context of formal methods applied to the
certification of critical software: the verification of the compiler guarantees
that the safety properties proved on the source code hold for the executable
compiled code as well
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