38,883 research outputs found
The Emergence of Anticommuting Coordinates and the Dirac-Ramond-Kostant operators
The history of anticommuting coordinates is decribed.Comment: 14 pages, Contribution to the Proceedings of The Gunnar Nordstr\"om
Symposium on Theoretical Physics - The Physics of Extra Dimension
Spacetime Encodings IV - The Relationship between Weyl Curvature and Killing Tensors in Stationary Axisymmetric Vacuum Spacetimes
The problem of obtaining an explicit representation for the fourth invariant
of geodesic motion (generalized Carter constant) of an arbitrary stationary
axisymmetric vacuum spacetime generated from an Ernst Potential is considered.
The coupling between the non-local curvature content of the spacetime as
encoded in the Weyl tensor, and the existence of a Killing tensor is explored
and a constructive, algebraic test for a fourth order Killing tensor suggested.
The approach used exploits the variables defined for the B\"{a}ckland
transformations to clarify the relationship between Weyl curvature, constants
of geodesic motion, expressed as Killing tensors, and the solution generation
techniques. A new symmetric non-covariant formulation of the Killing equations
is given. This formulation transforms the problem of looking for fourth-order
Killing tensors in 4D into one of looking for four interlocking two-manifolds
admitting fourth-order Killing tensors in 2D.Comment: 15 page
Frontier Economics: Why Entrepreneurial Capitalism Is Needed Now More Than Ever
Examines the roles of imitative and innovative economic growth and public policy in developed and developing economies in the twentieth century. Outlines role of uncertainty and economic freedom as drivers of innovation, competition, and continued growth
Maximally Supersymmetric Yang-Mills Theory. The Story of N = 4 Yang-Mills Theory
This is a personally colored account of the history behind N=4 Yang-Mills
Theory.Comment: Talk given at "60 years of Yang-Mills Theory", Singapore May 25-28,
2015. 15 page
Particle Physics as Representations of the Poincare Algebra
Eugene Wigner showed already in 1939 that the elementary particles are
related to the irreducible representations of the Poincare algebra. In the
light-cone frame formulation of quantum field theory one can extend these
representations to depend also on a coupling constant. The representations then
become non-linear and contain the interaction terms which are shown to have
strong uniqueness. Extending the algebra to supersymmetry it is shown that two
field theories stick out, N=4 Yang-Mills and N=8 Supergravity and their higher
dimensional analogues. I also discuss string theory from this starting point.Comment: Lecture presented at the Poincare Symposium held in Brussels on
October 8-9, 200
Maximal supersymmetry and exceptional groups
The article is a tribute to my old mentor, collaborator and friend Murray
Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself
where we describe the N = 8 Supergravity in the light-cone formalism. We show
how the Cremmer-Julia E7(7) non-linear symmetry is implemented and how the full
supermultiplet is a representation of the E7(7) symmetry. I also show how the
E7(7) symmetry is a key to understand the higher order couplings in the theory
and is very useful when we discuss possible counterterms for this theory.Comment: Proceedings of Conference in Honour of Murray Gell-Mann's 80th
Birthda
Spacetime Encodings III - Second Order Killing Tensors
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV)
spacetimes that were found by Carter to have separable Hamilton-Jacobi
equations, and thus admit a second-order Killing tensor. The derivation of the
spacetimes presented in this paper borrows from ideas about dynamical systems,
and illustrates concepts that can be generalized to higher- order Killing
tensors. The relationship between the components of the Killing equations and
metric functions are given explicitly. The origin of the four separable
coordinate systems found by Carter is explained and classified in terms of the
analytic structure associated with the Killing equations. A geometric picture
of what the orbital invariants may represent is built. Requiring that a SAV
spacetime admits a second-order Killing tensor is very restrictive, selecting
very few candidates from the group of all possible SAV spacetimes. This
restriction arises due to the fact that the consistency conditions associated
with the Killing equations require that the field variables obey a second-order
differential equation, as opposed to a fourth-order differential equation that
imposes the weaker condition that the spacetime be SAV. This paper introduces
ideas that could lead to the explicit computation of more general orbital
invariants in the form of higher-order Killing Tensors.Comment: 9 page
Balancing stress and recovery in sports
To reach elite level in sports, athletes have to start their intensive and time-consuming training at an early stage. The road to the top is a stressful one, not only due to the physiological stress of training, but also caused by psychological and social stress. In order to improve performance athletes continuously challenge their personal boundaries. This may lead to a local or general overload of the human body that results into injuries, illnesses and overtraining. Overtraining is characterized by an unexplained decrement in sport-specific performance and is often coupled with symptoms such as increased fatigue, poor concentration, disturbed mood, and altered eating and sleeping patterns. Full recovery may take months to years. Monitoring stress and recovery may help to optimize performance and prevent a local or general overload. Clinical measurements showed that mood state and hormonal responses to a double maximal exercise protocol provided valuable information to confirm the diagnosis of overtraining.
Orbital-Peierls State in NaTiSi2O6
Does the quasi one-dimensional titanium pyroxene NaTiSi2O6 exhibit the novel
{\it orbital-Peierls} state? We calculate its groundstate properties by three
methods: Monte Carlo simulations, a spin-orbital decoupling scheme and a
mapping onto a classical model. The results show univocally that for the spin
and orbital ordering to occur at the same temperature --an experimental
observation-- the crystal field needs to be small and the orbitals are active.
We also find that quantum fluctuations in the spin-orbital sector drive the
transition, explaining why canonical bandstructure methods fail to find it. The
conclusion that NaTiSi2O6 shows an orbital-Peierls transition is therefore
inevitable.Comment: 4 pages, 3 figure
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