6,469 research outputs found
Quantum Group Covariance and the Braided Structure of Deformed Oscillators
The connection between braided Hopf algebra structure and the quantum group
covariance of deformed oscillators is constructed explicitly. In this context
we provide deformations of the Hopf algebra of functions on SU(1,1). Quantum
subgroups and their representations are also discussed.Comment: 12 pages, to be published in JM
Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls
We extend our previous results of simplified expressions for functional
determinants for radial Schr\"odinger operators to the computation of vacuum
energy, or mass corrections, for static but spatially radial backgrounds, and
for domain wall configurations. Our method is based on the zeta function
approach to the Gel'fand-Yaglom theorem, suitably extended to higher
dimensional systems on separable manifolds. We find new expressions that are
easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page
Braided Oscillators
The braided Hopf algebra structure of the generalized oscillator is
investigated. Using the solutions two types of braided Fibonacci oscillators
are introduced. This leads to two types of braided Biedenharn-Macfarlane
oscillators.Comment: 12 pages, latex, some references added, published versio
Self-DUal SU(3) Chern-Simons Higgs Systems
We explore self-dual Chern-Simons Higgs systems with the local and
global symmetries where the matter field lies in the adjoint
representation. We show that there are three degenerate vacua of different
symmetries and study the unbroken symmetry and particle spectrum in each
vacuum. We classify the self-dual configurations into three types and study
their properties.Comment: Columbia Preprint CU-TP-635, 19 page
Understanding thermal alleviation in cold dwell fatigue in titanium alloys
Dwell fatigue facet nucleation has been investigated in isothermal rig disc spin tests and under anisothermal in-service engine conditions in titanium alloy IMI834 using α-HCP homogenised and faithful α-β lamellar microstructure crystal plasticity representations. The empirically observed facet nucleation and disc failure at low stress in the isothermal spin tests has been explained and originates from the material rate sensitivity giving rise to soft grain creep accumulation and hard grain basal stresses which increase with fatigue cycling until facet nucleation. The α-HCP homogenised model is not able to capture this observed behaviour at sensible applied stresses. In contrast to the isothermal spin tests, anisothermal in-service disc loading conditions generate soft grain slip accumulation predominantly in the first loading cycle after which no further load shedding nor soft grain creep accumulation is observed, such that the behaviour is stable, with no further increase in hard grain basal stress so that facet nucleation does not occur, as observed empirically. The thermal alleviation, which derives from in-service loading conditions and gives the insensitivity to dwell fatigue dependent on the temperature excursions, has been explained. A stress-temperature map for IMI834 alloy has been established to demarcate the ranges for which the propensity for dwell fatigue facet nucleation is high, threatening or low
Functional Determinants in Quantum Field Theory
Functional determinants of differential operators play a prominent role in
theoretical and mathematical physics, and in particular in quantum field
theory. They are, however, difficult to compute in non-trivial cases. For one
dimensional problems, a classical result of Gel'fand and Yaglom dramatically
simplifies the problem so that the functional determinant can be computed
without computing the spectrum of eigenvalues. Here I report recent progress in
extending this approach to higher dimensions (i.e., functional determinants of
partial differential operators), with applications in quantum field theory.Comment: Plenary talk at QTS5 (Quantum Theory and Symmetries); 16 pp, 2 fig
Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories
An algebraic method is used to work out the mass spectra and symmetry
breaking patterns of general vacuum states in N=2 supersymmetric SU(n)
Chern-Simons-Higgs systems with the matter fields being in the adjoint
representation. The approach provides with us a natural basis for fields, which
will be useful for further studies in the self-dual solutions and quantum
corrections. As the vacuum states satisfy the SU(2) algebra, it is not
surprising to find that their spectra are closely related to that of angular
momentum addition in quantum mechanics. The analysis can be easily generalized
to other classical Lie groups.Comment: 17 pages, use revte
Chern-Simons Solitons, Toda Theories and the Chiral Model
The two-dimensional self-dual Chern--Simons equations are equivalent to the
conditions for static, zero-energy solutions of the -dimensional gauged
nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In
this paper we classify all finite charge solutions by first
transforming the self-dual Chern--Simons equations into the two-dimensional
chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood
classification of harmonic maps into the unitary groups. This construction also
leads to a new relationship between the Toda and chiral model
solutions
Derivative expansion and large gauge invariance at finite temperature
We study the 0+1 dimensional Chern-Simons theory at finite temperature within
the framework of derivative expansion. We obtain various interesting relations,
solve the theory within this framework and argue that the derivative expansion
is not a suitable formalism for a study of the question of large gauge
invariance.Comment: 12 pages, Late
Abelian Toda field theories on the noncommutative plane
Generalizations of GL(n) abelian Toda and abelian affine
Toda field theories to the noncommutative plane are constructed. Our proposal
relies on the noncommutative extension of a zero-curvature condition satisfied
by algebra-valued gauge potentials dependent on the fields. This condition can
be expressed as noncommutative Leznov-Saveliev equations which make possible to
define the noncommutative generalizations as systems of second order
differential equations, with an infinite chain of conserved currents. The
actions corresponding to these field theories are also provided. The special
cases of GL(2) Liouville and sinh/sine-Gordon are
explicitly studied. It is also shown that from the noncommutative
(anti-)self-dual Yang-Mills equations in four dimensions it is possible to
obtain by dimensional reduction the equations of motion of the two-dimensional
models constructed. This fact supports the validity of the noncommutative
version of the Ward conjecture. The relation of our proposal to previous
versions of some specific Toda field theories reported in the literature is
presented as well.Comment: v3 30 pages, changes in the text, new sections included and
references adde
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