45 research outputs found
Ariel - Volume 9 Number 5
Executive Editor
Seth B. Paul
Associate Editor
Warren J. Ventriglia
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Fredric Jay Matlin
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John Patrick Welch
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Brenda Peterso
G<sub>2</sub>-structures and quantization of non-geometric M-theory backgrounds
We describe the quantization of a four-dimensional locally non-geometric
M-theory background dual to a twisted three-torus by deriving a phase space
star product for deformation quantization of quasi-Poisson brackets related to
the nonassociative algebra of octonions. The construction is based on a choice
of -structure which defines a nonassociative deformation of the addition
law on the seven-dimensional vector space of Fourier momenta. We demonstrate
explicitly that this star product reduces to that of the three-dimensional
parabolic constant -flux model in the contraction of M-theory to string
theory, and use it to derive quantum phase space uncertainty relations as well
as triproducts for the nonassociative geometry of the four-dimensional
configuration space. By extending the -structure to a -structure,
we propose a 3-algebra structure on the full eight-dimensional M2-brane phase
space which reduces to the quasi-Poisson algebra after imposing a particular
gauge constraint, and whose deformation quantisation simultaneously encompasses
both the phase space star products and the configuration space triproducts. We
demonstrate how these structures naturally fit in with previous occurences of
3-algebras in M-theory.Comment: 41 pages; v2: Final version published in JHE
Nothing Lasts Forever: Environmental Discourses on the Collapse of Past Societies
The study of the collapse of past societies raises many questions for the theory and practice of archaeology. Interest in collapse extends as well into the natural sciences and environmental and sustainability policy. Despite a range of approaches to collapse, the predominant paradigm is environmental collapse, which I argue obscures recognition of the dynamic role of social processes that lie at the heart of human communities. These environmental discourses, together with confusion over terminology and the concepts of collapse, have created widespread aporia about collapse and resulted in the creation of mixed messages about complex historical and social processes