7,304 research outputs found
Conformal Designs based on Vertex Operator Algebras
We introduce the notion of a conformal design based on a vertex operator
algebra. This notation is a natural analog of the notion of block designs or
spherical designs when the elements of the design are based on self-orthogonal
binary codes or integral lattices, respectively. It is shown that the subspaces
of fixed degree of an extremal self-dual vertex operator algebra form conformal
11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and
Venkov for extremal doubly-even codes and extremal even lattices. Other
examples are coming from group actions on vertex operator algebras, the case
studied first by Matsuo. The classification of conformal 6- and 8-designs is
investigated. Again, our results are analogous to similar results for codes and
lattices.Comment: 35 pages with 1 table, LaTe
Switching internal times and a new perspective on the 'wave function of the universe'
Despite its importance in general relativity, a quantum notion of general
covariance has not yet been established in quantum gravity and cosmology,
where, given the a priori absence of coordinates, it is necessary to replace
classical frames with dynamical quantum reference systems. As such, quantum
general covariance bears on the ability to consistently switch between the
descriptions of the same physics relative to arbitrary choices of quantum
reference system. Recently, a systematic approach for such switches has been
developed (arXiv:1809.00556, 1809.05093, 1810.04153). It links the descriptions
relative to different choices of quantum reference system, identified as the
correspondingly reduced quantum theories, via the reference-system-neutral
Dirac quantization, in analogy to coordinate changes on a manifold. In this
work, we apply this method to a simple cosmological model to demonstrate how to
consistently switch between different internal time choices in quantum
cosmology. We substantiate the argument that the conjunction of Dirac and
reduced quantized versions of the theory defines a complete relational quantum
theory that not only admits a quantum general covariance, but, we argue, also
suggests a new perspective on the 'wave function of the universe'. It assumes
the role of a perspective-neutral global state, without immediate physical
interpretation, that, however, encodes all the descriptions of the universe
relative to all possible choices of reference system at once and constitutes
the crucial link between these internal perspectives. While, for simplicity, we
use the Wheeler-DeWitt formulation, the method and arguments might be also
adaptable to loop quantum cosmology.Comment: 14+7 pages. Invited contribution to the special issue "Progress in
Group Field Theory and Related Quantum Gravity Formalisms", Eds. S. Carrozza,
S. Gielen and D. Oriti. Minor clarifications, updated references, matches
published versio
Ethics and the moral life
The article summarizes recent social scientific studies of the moral life, and pedogogies for moral education, in their relation to normative inquiry (ethics). Particular attention is paid to values clarification, situational (behavioral) studies, the developmental studies of Piaget and Kohlberg, and the author\u27s own phenomenological research on moral consciousness
Quantization of systems with temporally varying discretization I: Evolving Hilbert spaces
A temporally varying discretization often features in discrete gravitational
systems and appears in lattice field theory models subject to a coarse graining
or refining dynamics. To better understand such discretization changing
dynamics in the quantum theory, an according formalism for constrained
variational discrete systems is constructed. While the present manuscript
focuses on global evolution moves and, for simplicity, restricts to Euclidean
configuration spaces, a companion article discusses local evolution moves. In
order to link the covariant and canonical picture, the dynamics of the quantum
states is generated by propagators which satisfy the canonical constraints and
are constructed using the action and group averaging projectors. This projector
formalism offers a systematic method for tracing and regularizing divergences
in the resulting state sums. Non-trivial coarse graining evolution moves lead
to non-unitary, and thus irreversible, projections of physical Hilbert spaces
and Dirac observables such that these concepts become evolution move dependent
on temporally varying discretizations. The formalism is illustrated in a toy
model mimicking a `creation from nothing'. Subtleties arising when applying
such a formalism to quantum gravity models are discussed.Comment: 45 pages, 1 appendix, 6 figures (additional explanations, now matches
published version
Canonical linearized Regge Calculus: counting lattice gravitons with Pachner moves
We afford a systematic and comprehensive account of the canonical dynamics of
4D Regge Calculus perturbatively expanded to linear order around a flat
background. To this end, we consider the Pachner moves which generate the most
basic and general simplicial evolution scheme. The linearized regime features a
vertex displacement (`diffeomorphism') symmetry for which we derive an abelian
constraint algebra. This permits to identify gauge invariant `lattice
gravitons' as propagating curvature degrees of freedom. The Pachner moves admit
a simple method to explicitly count the gauge and `graviton' degrees of freedom
on an evolving triangulated hypersurface and we clarify the distinct role of
each move in the dynamics. It is shown that the 1-4 move generates four `lapse
and shift' variables and four conjugate vertex displacement generators; the 2-3
move generates a `graviton'; the 3-2 move removes one `graviton' and produces
the only non-trivial equation of motion; and the 4-1 move removes four `lapse
and shift' variables and trivializes the four conjugate symmetry generators. It
is further shown that the Pachner moves preserve the vertex displacement
generators. These results may provide new impetus for exploring `graviton
dynamics' in discrete quantum gravity models.Comment: 26+13 pages, 2 appendices, many figures. References updated, small
clarifications added. This article is fairly self-containe
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