2,712 research outputs found
Scaling algebras and pointlike fields: A nonperturbative approach to renormalization
We present a method of short-distance analysis in quantum field theory that
does not require choosing a renormalization prescription a priori. We set out
from a local net of algebras with associated pointlike quantum fields. The net
has a naturally defined scaling limit in the sense of Buchholz and Verch; we
investigate the effect of this limit on the pointlike fields. Both for the
fields and their operator product expansions, a well-defined limit procedure
can be established. This can always be interpreted in the usual sense of
multiplicative renormalization, where the renormalization factors are
determined by our analysis. We also consider the limits of symmetry actions. In
particular, for suitable limit states, the group of scaling transformations
induces a dilation symmetry in the limit theory.Comment: minor changes and clarifications; as to appear in Commun. Math.
Phys.; 37 page
Consistent histories and relativistic invariance in the modal interpretation of quantum mechanics
Modal interpretations of quantum mechanics assign definite properties to
physical systems and specify single-time joint probabilities of these
properties. We show that a natural extension, applying to properties at several
times, can be given if a decoherence condition is satisfied. This extension
defines "consistent histories" of modal properties. We suggest a new form of
the modal scheme, that offers prospects of a more general applicability of the
histories concept. Finally, we discuss a possible way of applying these ideas
to relativistic quantum field theory.Comment: 13 pages, no figure
A geometrical origin for the covariant entropy bound
Causal diamond-shaped subsets of space-time are naturally associated with
operator algebras in quantum field theory, and they are also related to the
Bousso covariant entropy bound. In this work we argue that the net of these
causal sets to which are assigned the local operator algebras of quantum
theories should be taken to be non orthomodular if there is some lowest scale
for the description of space-time as a manifold. This geometry can be related
to a reduction in the degrees of freedom of the holographic type under certain
natural conditions for the local algebras. A non orthomodular net of causal
sets that implements the cutoff in a covariant manner is constructed. It gives
an explanation, in a simple example, of the non positive expansion condition
for light-sheet selection in the covariant entropy bound. It also suggests a
different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio
Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
We give a scheme for interpreting shaded tangles as quantum programs, with
the property that isotopic tangles yield equivalent programs. We analyze many
known quantum programs in this way -- including entanglement manipulation and
error correction -- and in each case present a fully-topological formal
verification, yielding in several cases substantial new insight into how the
program works. We also use our methods to identify several new or generalized
procedures.Comment: In Proceedings QPL 2017, arXiv:1802.0973
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