96 research outputs found
Quantum Harmonic Oscillator as a Zariski Geometry
We carry out a model-theoretic analysis of the Heisenberg algebra. To this
end, a geometric structure is associated to the Heisenberg algebra and is shown
to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be
non-classical, in the sense that it is not interpretable in an algebraically
closed field. On assuming self-adjointness of the position and momentum
operators, one obtains a discrete substructure of which the original Zariski
geometry is seen as the complexification.Comment: some typos correcte
Equivariant Zariski Structures
A new class of noncommutative -algebras (for an algebraically closed
field) is defined and shown to contain some important examples of quantum
groups. To each such algebra, a first order theory is assigned describing
models of a suitable corresponding geometric space. Model-theoretic results for
these geometric structures are established (uncountable categoricity,
quantifier elimination to the level of existential formulas) and that an
appropriate dimension theory exists, making them Zariski structures
The Arithmetic of Fields
This is the report on the Oberwolfach workshop The Arithmetic of Fields, held in February 2006. Field Arithmetic (MSC 12E30) is a branch of mathematics concerned with studying the inner structure (orderings, valuations, arithmetic, diophantine properties) of fields and their algebraic extensions using Galois theory, algebraic geometry and number theory, partially in connection with model theoretical methods from mathematical logic
Field Arithmetic
Field Arithmetic studies the interrelation between arithmetic properties of fields and their absolute Galois groups. It is an interdisciplinary area that uses methods of algebraic number theory, commutative algebra, algebraic geometry, arithmetic geometry, finite and profinite groups, and nonarchimedean analysis. Some of the results are motivated by questions of model theory and used to establish results in (un-)decidability
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