12,739 research outputs found
A Riccati type PDE for light-front higher helicity vertices
This paper is based on a curious observation about an equation related to the
tracelessness constraints of higher spin gauge fields. The equation also occurs
in the theory of continuous spin representations of the Poincar\'e group.
Expressed in an oscillator basis for the higher spin fields, the equation
becomes a non-linear partial differential operator of the Riccati type acting
on the vertex functions. The consequences of the equation for the cubic vertex
is investigated in the light-front formulation of higher spin theory. The
classical vertex is completely fixed but there is room for off-shell quantum
corrections.Comment: 27 pages. Updated to published versio
Impurity effects at finite temperature in the two-dimensional S=1/2 Heisenberg antiferromagnet
We discuss effects of various impurities on the magnetic susceptibility and
the specific heat of the quantum S=1/2 Heisenberg antiferromagnet on a
two-dimensional square lattice. For impurities with spin S_i > 0 (here S_i=1/2
in the case of a vacancy or an added spin, and S_i=1 for a spin coupled
ferromagnetically to its neighbors), our quantum Monte Carlo simulations
confirm a classical-like Curie susceptibility contribution S_i^2/4T, which
originates from an alignment of the impurity spin with the local N\'eel order.
In addition, we find a logarithmically divergent contribution, which we
attribute to fluctuations transverse to the local N\'eel vector. We also study
frustrated and nonfrustrated bond impurities with S_i=0. For a simple intuitive
picture of the impurity problem, we discuss an effective few-spin model that
can distinguish between the different impurities and reproduces the
leading-order simulation data over a wide temperature range.Comment: 15 pages, 14 figures, submitted to PRB. v2, published version with
cosmetic change
Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity
In this paper we discuss gravity in the light-front formulation (light-cone
gauge) and show how possible counterterms arise. We find that Poincare
invariance is not enough to find the three-point counterterms uniquely.
Higher-spin fields can intrude and mimic three-point higher derivative gravity
terms. To select the correct term we have to use the remaining
reparametrization invariance that exists after the gauge choice. We finally
sketch how the corresponding programme for N=8 Supergravity should work.Comment: 26 pages, references added, published versio
Liberal Arts Inspired Mathematics: A Report OR How to bring cultural and humanistic aspects of mathematics to the classroom as effective teaching and learning tools
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the is algebra necessary?\u27\u27 discussion, teaching mathematics as a language, the transfer problem in learning, and the relationship between humanistic mathematics and mathematics as taught in liberal arts contexts
Towards Unifying Structures in Higher Spin Gauge Symmetry
This article is expository in nature, outlining some of the many still
incompletely understood features of higher spin field theory. We are mainly
considering higher spin gauge fields in their own right as free-standing
theoretical constructs and not circumstances where they occur as part of
another system. Considering the problem of introducing interactions among
higher spin gauge fields, there has historically been two broad avenues of
approach. One approach entails gauging a non-Abelian global symmetry algebra,
in the process making it local. The other approach entails deforming an already
local but Abelian gauge algebra, in the process making it non-Abelian. In cases
where both avenues have been explored, such as for spin 1 and 2 gauge fields,
the results agree (barring conceptual and technical issues) with Yang-Mills
theory and Einstein gravity. In the case of an infinite tower of higher spin
gauge fields, the first approach has been thoroughly developed and explored by
M. Vasiliev, whereas the second approach, after having lain dormant for a long
time, has received new attention by several authors lately. In the present
paper we briefly review some aspects of the history of higher spin gauge fields
as a backdrop to an attempt at comparing the gauging vs. deforming approaches.
A common unifying structure of strongly homotopy Lie algebras underlying both
approaches will be discussed. The modern deformation approach, using BRST-BV
methods, will be described as far as it is developed at the present time. The
first steps of a formulation in the categorical language of operads will be
outlined. A few aspects of the subject that seems not to have been thoroughly
investigated are pointed out.Comment: This is a contribution to the Proc. of the Seventh International
Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007,
Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
A proposal to determine properties of the gravitropic response of plants in the absence of a complicating g-force (GTHRES)
Gravitropic responses of oat seedlings (Avena sativa L.) were measured on Earth and in microgravity (IML-1). The seedlings were grown at 1 g either on Earth or on 1 g centrifuges. They were challenged by centripetal accelerations for which the intensity and duration of the stimulations were varied. All stimulation intensities were in the hypogravity region from 0.1 to 1.0 g. All responses occurred either in Spacelab microgravity or during clinorotation on Earth. The experiments were carried out with the same apparatus in Spacelab and on Earth. The experiments addressed a series of scientific questions and useful data were obtained to provide answers to some but not all of those questions
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