52,489 research outputs found
Existence of Local Covariant Time Ordered Products of Quantum Fields in Curved Spacetime
We establish the existence of local, covariant time ordered products of local
Wick polynomials for a free scalar field in curved spacetime. Our time ordered
products satisfy all of the hypotheses of our previous uniqueness theorem, so
our construction essentially completes the analysis of the existence,
uniqueness and renormalizability of the perturbative expansion for nonlinear
quantum field theories in curved spacetime. As a byproduct of our analysis, we
derive a scaling expansion of the time ordered products about the total
diagonal that expresses them as a sum of products of polynomials in the
curvature times Lorentz invariant distributions, plus a remainder term of
arbitrary low scaling degree.Comment: Minor revisions, 2 references added. 43 pages, Latex format, no
figure
Driven Dynamics of Periodic Elastic Media in Disorder
We analyze the large-scale dynamics of vortex lattices and charge density
waves driven in a disordered potential. Using a perturbative coarse-graining
procedure we present an explicit derivation of non-equilibrium terms in the
renormalized equation of motion, in particular Kardar-Parisi-Zhang
non-linearities and dynamic strain terms. We demonstrate the absence of glassy
features like diverging linear friction coefficients and transverse critical
currents in the drifting state. We discuss the structure of the dynamical phase
diagram containing different elastic phases very small and very large drive and
plastic phases at intermediate velocity.Comment: 21 pages Latex with 4 figure
Quantum Field Theory Is Not Merely Quantum Mechanics Applied to Low Energy Effective Degrees of Freedom
It is commonly assumed that quantum field theory arises by applying ordinary
quantum mechanics to the low energy effective degrees of freedom of a more
fundamental theory defined at ultra-high-energy/short-wavelength scales. We
shall argue here that, even for free quantum fields, there are holistic aspects
of quantum field theory that cannot be properly understood in this manner.
Specifically, the ``subtractions'' needed to define nonlinear polynomial
functions of a free quantum field in curved spacetime are quite simple and
natural from the quantum field theoretic point of view, but are at best
extremely ad hoc and unnatural if viewed as independent renormalizations of
individual modes of the field. We illustrate this point by contrasting the
analysis of the Casimir effect, the renormalization of the stress-energy tensor
in time-dependent spacetimes, and anomalies from the point of quantum field
theory and from the point of view of quantum mechanics applied to the
independent low energy modes of the field. Some implications for the
cosmological constant problem are discussed.Comment: Latex, 8 Pages, 5th Prize Essay, Gravity Research Foundatio
An Alternative to Inflation
Inflationary models are generally credited with explaining the large scale
homogeneity, isotropy, and flatness of our universe as well as accounting for
the origin of structure (i.e., the deviations from exact homogeneity) in our
universe. We argue that the explanations provided by inflation for the
homogeneity, isotropy, and flatness of our universe are not satisfactory, and
that a proper explanation of these features will require a much deeper
understanding of the initial state of our universe. On the other hand,
inflationary models are spectacularly successful in providing an explanation of
the deviations from homogeneity. We point out here that the fundamental
mechanism responsible for providing deviations from homogeneity -- namely, the
evolutionary behavior of quantum modes with wavelength larger than the Hubble
radius -- will operate whether or not inflation itself occurs. However, if
inflation did not occur, one must directly confront the issue of the initial
state of modes whose wavelength was larger than the Hubble radius at the time
at which they were "born". Under some simple hypotheses concerning the "birth
time" and initial state of these modes (but without any "fine tuning"), it is
shown that non-inflationary fluid models in the extremely early universe would
result in the same density perturbation spectrum and amplitude as inflationary
models, although there would be no "slow roll" enhancement of the scalar modes.Comment: 4th Prize Gravity Research Foundation essay, with minor revisions and
a number of additional footnotes. 12 pages, Latex, no figure
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