506 research outputs found
What is an elementary particle?
Schrödinger discusses what an elementary particle is. This essay originally appeared in the journal Endeavour
Einstein's Boxes
At the 1927 Solvay conference, Einstein presented a thought experiment
intended to demonstrate the incompleteness of the quantum mechanical
description of reality. In the following years, the thought experiment was
picked up and modified by Einstein, de Broglie, and several other commentators
into a simple scenario involving the splitting in half of the wave function of
a single particle in a box. In this paper we collect together several
formulations of this thought experiment from the existing literature; analyze
and assess it from the point of view of the Einstein-Bohr debates, the EPR
dilemma, and Bell's theorem; and generally lobby for Einstein's Boxes taking
its rightful place alongside similar but historically better-known quantum
mechanical thought experiments such as EPR and Schroedinger's Cat.Comment: Published versio
Gauge theories on noncommutative euclidean spaces
We consider gauge theories on noncommutative euclidean space . In particular,
we discuss the structure of gauge group following standard mathematical
definitions and using the ideas of hep-th/0102182.Comment: Corrections made, references adde
Compact Kac algebras and commuting squares
We consider commuting squares of finite dimensional von Neumann algebras
having the algebra of complex numbers in the lower left corner. Examples
include the vertex models, the spin models (in the sense of subfactor theory)
and the commuting squares associated to finite dimensional Kac algebras. To any
such commuting square we associate a compact Kac algebra and we compute the
corresponding subfactor and its standard invariant in terms of it.Comment: 14 pages, some minor change
Infinite random matrices and ergodic measures
We introduce and study a 2-parameter family of unitarily invariant
probability measures on the space of infinite Hermitian matrices. We show that
the decomposition of a measure from this family on ergodic components is
described by a determinantal point process on the real line. The correlation
kernel for this process is explicitly computed.
At certain values of parameters the kernel turns into the well-known sine
kernel which describes the local correlation in Circular and Gaussian Unitary
Ensembles. Thus, the random point configuration of the sine process is
interpreted as the random set of ``eigenvalues'' of infinite Hermitian matrices
distributed according to the corresponding measure.Comment: 36 page
Deformation Theory of Infinity Algebras
This work explores the deformation theory of algebraic structures in a very
general setting. These structures include commutative, associative algebras,
Lie algebras, and the infinity versions of these structures, the strongly
homotopy associative and Lie algebras. In all these cases the algebra structure
is determined by an element of a certain graded Lie algebra which plays the
role of a differential on this algebra. We work out the deformation theory in
terms of the Lie algebra of coderivations of an appropriate coalgebra structure
and construct a universal infinitesimal deformation as well as a miniversal
formal deformation. By working at this level of generality, the main ideas
involved in deformation theory stand out more clearly.Comment: 31 pages, LaTeX2
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