* Idea: A diagrammatic way of describing representations of finite and compact Lie groups.
* Examples: For SU(n), denoting the fundamental representation by a box
and the conjugate
one by a column of n–1 boxes,
we get:Topics, Y
Yamabe Invariant
@ References: Botvinnik & Rosenberg JDG(02)
[non-simply connected manifolds]; Avila & Dain CQG(08) [axisymmetric initial
data of two Kerr black holes].
Yamabe Question
@ Solution: Schoen JDG(84).
Yang-Baxter Equation > s.a. integrable
systems; lie algebras.
* Remark: The solutions
of the YB equation "at roots of unity" are related to algebraic
curves of genus > 1; They are also known to be connected with the "chiral
Potts model".
@ General references: Korepanov in(86)nl/00;
Jimbo IJMPA(89)
[intro]; Babelon & Viallet pr(89); Perk & Au-Yang mp/06-in
[rev].
@ Generalizations: Ambjørn et al NPB(06) [3D, Zamolodchikov's tetrahedron equations,
simplified].
Yano Tensor
@ References: Cariglia CQG(04)ht/03 [and
Dirac equation in curved spacetime].
Yarkovsky Effect > s.a. Asteroids.
* Idea: A non-gravitational
force acting on asteroids, arising from recoil
due to re-emission of heat absorbed from the Sun.
@ References: Lorenz & Spitale Icarus(04)
[as heat engine]; news BBC(07)mar,
pw(07)mar
[observation].
Yilmaz Theory
* Idea: An alternative,
4D, curved spacetime theory of gravity, in which the Ricci curvature is defined
in terms of a massless Klein-Gordon scalar field on an initially flat spacetime,
and satisfies the Einstein equation with the usual scalar field stress-energy
tensor;
Predicts the existence of N-body
interacting solutions without event horizons.
@ References: Yilmaz PR(58),
comment Hoffmann JMM(60); Misner NCB(99)gq/95;
Alley & Yilmaz NCB(99)gq/95;
Wyss NCB(99); Alley et al ap/99/ApJL;
Ibison CQG(06)-a0705 [FRW
models].
Young Tableaux > s.a. group
representations.
* Idea: A diagrammatic way of describing representations of finite
and compact Lie groups.
* Examples: For SU(n), denoting the fundamental representation
by a box and the conjugate
one by a column of n–1 boxes,
we get:
* Dimension: The dimension
of such a representation can be calculated as follows: ...
@ References: Hamermesh 63; Fulton 97 [applications to representation
theory and geometry].
Young's Double Slit Experiment > see experiments in physics; Interference.
Yukawa Potential > s.a. renormalization [Yukawa theories with fermions].
* Idea: An exponential
potential U(r) = exp(–r/
)/r,
introduced by Yukawa to describe a meson-mediated interaction, where the length
scale is related to
the mass of the particle.
@ References: Gönül et al PS(06)
[quantum, eigenvalues and eigenfunctions]; > s.a. chaotic
systems.
> And gravity: see modified newtonian gravity and
tests.
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send feedback and suggestions to bombelli at olemiss.edu – modified
23 dec 2008