598 research outputs found
`Iconoclastic', Categorical Quantum Gravity
This is a two-part, `2-in-1' paper. In Part I, the introductory talk at
`Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international
theoretical physics conference is presented in paper form (without references).
In Part II, the more technical talk, originally titled ``Abstract Differential
Geometric Excursion to Classical and Quantum Gravity'', is presented in paper
form (with citations). The two parts are closely entwined, as Part I makes
general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic
Approaches to Quantum Gravity'' international theoretical physics conference,
Athens, Greece (summer 2004
Infinity
This essay surveys the different types of infinity that occur in pure and applied mathematics, with emphasis on: 1. the contrast between potential infinity and actual infinity; 2. Cantor's distinction between transfinite sets and absolute infinity; 3. the constructivist view of infinite quantifiers and the meaning of constructive proof; 4. the concept of feasibility and the philosophical problems surrounding feasible arithmetic; 5. Zeno's paradoxes and modern paradoxes of physical infinity involving supertasks
`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories
Based on the algebraico-categorical (:sheaf-theoretic and sheaf
cohomological) conceptual and technical machinery of Abstract Differential
Geometry, a new, genuinely background spacetime manifold independent, field
quantization scenario for vacuum Einstein gravity and free Yang-Mills theories
is introduced. The scheme is coined `third quantization' and, although it
formally appears to follow a canonical route, it is fully covariant, because it
is an expressly functorial `procedure'. Various current and future Quantum
Gravity research issues are discussed under the light of 3rd-quantization. A
postscript gives a brief account of this author's personal encounters with
Rafael Sorkin and his work.Comment: 43 pages; latest version contributed to a fest-volume celebrating
Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly
written that the Editor for this volume is Daniele Oriti, with CUP as
publisher. I apologize for the mistake.
Quantum evolution of scalar fields in Robertson-Walker space-time
We study the field theory in a flat Robertson-Walker
space-time using the functional Sch\"odinger picture. We introduce a simple
Gaussian approximation to analyze the time evolution of pure states and we
establish the renormalizability of the approximation. We also show that the
energy-momentum tensor in this approximation is finite once we consider the
usual mass and coupling constant renormalizations.Comment: Revtex file, 19 pages, no figures. Compressed ps version available at
http://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-912.ps.Z or at
ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-912.ps.
Introduction to Loop Quantum Gravity
This article is based on the opening lecture at the third quantum geometry
and quantum gravity school sponsored by the European Science Foundation and
held at Zakopane, Poland in March 2011. The goal of the lecture was to present
a broad perspective on loop quantum gravity for young researchers. The first
part is addressed to beginning students and the second to young researchers who
are already working in quantum gravity.Comment: 30 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:gr-qc/041005
Gravity and the Quantum
The goal of this article is to present a broad perspective on quantum gravity
for \emph{non-experts}. After a historical introduction, key physical problems
of quantum gravity are illustrated. While there are a number of interesting and
insightful approaches to address these issues, over the past two decades
sustained progress has primarily occurred in two programs: string theory and
loop quantum gravity. The first program is described in Horowitz's contribution
while my article will focus on the second. The emphasis is on underlying ideas,
conceptual issues and overall status of the program rather than mathematical
details and associated technical subtleties.Comment: A general review of quantum gravity addresed non-experts. To appear
in the special issue `Space-time Hundred Years Later' of NJP; J.Pullin and R.
Price (editors). Typos and an attribution corrected; a clarification added in
section 2.
The Nobel Prize in Physics 1999
The last Nobel Prize of the Millenium in Physics has been awarded jointly to
Professor Gerardus 't Hooft of the University of Utrecht in Holland and his
thesis advisor Professor Emeritus Martinus J.G. Veltman of Holland. According
to the Academy's citation, the Nobel Prize has been awarded for 'elucidating
the quantum structure of electroweak interaction in Physics'. It further goes
on to say that they have placed particle physics theory on a firmer
mathematical foundation. In this short note, we will try to understand both
these aspects of the award. The work for which they have been awarded the Nobel
Prize was done in 1971. However, the precise predictions of properties of
particles that were made possible as a result of their work, were tested to a
very high degree of accuracy only in this last decade. This was done in a
series of measurements in the experiments in the accelerator laboratories at
CERN (Geneva) and Fermilab. To understand the full significance of this Nobel
Prize, we will have to summarise briefly the developement of our current
theoretical framework about the basic constituents of matter and the forces
which hold them together. In fact the path can be partially traced in a chain
of Nobel prizes starting from one in 1965 to S. Tomonaga, J. Schwinger and R.
Feynman, to the one to S.L. Glashow, A. Salam and S. Weinberg in 1979, and then
to C. Rubia and Simon van der Meer in 1984 ending with the current one.Comment: 5 pages, LateX, no inline figures. Six 'boxes' included separately as
six jpg files. These jpg files as well as 10 separate pdf files (one for each
printed page) can be accessed from
http://144.16.74.196/~www/resonance/npp99res.htm. added journal re
Area spectrum of the Schwarzschild black hole
We consider a Hamiltonian theory of spherically symmetric vacuum Einstein
gravity under Kruskal-like boundary conditions in variables associated with the
Einstein-Rosen wormhole throat. The configuration variable in the reduced
classical theory is the radius of the throat, in a foliation that is frozen at
the left hand side infinity but asymptotically Minkowski at the right hand side
infinity, and such that the proper time at the throat agrees with the right
hand side Minkowski time. The classical Hamiltonian is numerically equal to the
Schwarzschild mass. Within a class of Hamiltonian quantizations, we show that
the spectrum of the Hamiltonian operator is discrete and bounded below, and can
be made positive definite. The large eigenvalues behave asymptotically
as~, where is an integer. The resulting area spectrum agrees
with that proposed by Bekenstein and others. Analogous results hold in the
presence of a negative cosmological constant and electric charge. The classical
input that led to the quantum results is discussed.Comment: 30 pages, REVTeX v3.0. (Minor additions, several added references.
Reduction, Emergence and Renormalization
In previous work, I described several examples combining reduction and
emergence: where reduction is understood a la Ernest Nagel, and emergence is
understood as behaviour or properties that are novel (by some salient
standard). Here, my aim is again to reconcile reduction and emergence, for a
case which is apparently more problematic than those I treated before:
renormalization.
Renormalization is a vast subject. So I confine myself to emphasizing how the
modern approach to renormalization (initiated by Wilson and others between 1965
and 1975), when applied to quantum field theories, illustrates both Nagelian
reduction and emergence. My main point is that the modern understanding of how
renormalizability is a generic feature of quantum field theories at accessible
energies gives us a conceptually unified family of Nagelian reductions.
That is worth saying since philosophers tend to think of scientific
explanation as only explaining an individual event, or perhaps a single law, or
at most deducing one theory as a special case of another. Here we see a
framework in which there is a space of theories endowed with enough structure
that it provides a family of reductions.Comment: 43 pages, no figure
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