246 research outputs found
Monopole-charge instability
For monopoles with nonvanishing Higgs potential it is shown that with respect
to "Brandt-Neri-Coleman type" variations (a) the stability problem reduces to
that of a pure gauge theory on the two-sphere (b) each topological sector
admits one, and only one, stable monopole charge, and (c) each unstable
monopole admits negative modes, where the sum goes over
all negative eigenvalues of the non-Abelian charge . An explicit
construction for (i) the unique stable charge (ii) the negative modes and (iii)
the spectrum of the Hessian, on the 2-sphere, is then given. The relation to
loops in the residual group is explained. The negative modes are tangent to
suitable energy-reducing two-spheres. The general theory is illustrated for the
little groups U(2), U(3), SU(3)/Z_3 and O(5).Comment: LaTex, 38 pages. 7 figures and 2 photos. Posted for the record.
Originally published 20 years ago, with Note added in 2009: Hommage to
Lochlainn O'Raifeartaigh and Sidney Coleman. Some typos correcte
The Problem of "Global Color" in Gauge Theories
The problem of “global color” (which arose recently in monopole theory) is generalized to arbitrary gauge theories: a subgroup K of the “unbroken” gauge group G is implementable iff the gauge bundle reduces to the centralizer of K in G. Equivalent implementations correspond to equivalent reductions. Such an action is an internal symmetry for a given configuration iff the Yang-Mills field reduces also. The case of monopoles is worked out in detail
On the stability of monopoles
A monopole with non-Abelian charge Q admits 2Σ|2α(Q)|-1 negative modes where α is a root of the residual group. These modes can be constructed by techniques of geometric quantization. Each topological sector admits a unique stable monopole
Inter-Annual Variability in Pasture Herbage Accumulation in Temperate Dairy Regions: Causes, Consequences, and Management Tools
Inter-annual variation in pasture herbage accumulation rate (HAR) is common in temperate dairy regions, posing challenges for farmers in the management of dairy cow feeding and of pasture state. This paper reviews the biophysical factors that cause inter-annual variation, considers some of its consequences for the efficient harvest of pasture, and discusses the basis for decision rules and support tools that are available to assist New Zealand and Australian farmers to help manage the consequences of an imbalance between feed supply and demand. These tools are well-grounded in scientific research and farmer experience, but are not widely used in the Australasian dairy industries. Some of the reasons for this are discussed. Inter-annual variability in HAR cannot be removed, even with inputs such as irrigation, but reliable forecasts of pasture HAR for a month or more could greatly improve the effectiveness of operational and tactical decision-making. Various approaches to pasture forecasting, based on pasture growth simulation models, are presented and discussed. Some of these appear to have reasonable predictive ability. However, considerably more development work is needed to: (1) prove their effectiveness; and (2) build the systems required to capture real-time, on farm data for critical systems variables such as pasture herbage mass and soil water content to combine with daily weather data. This technology presents an opportunity for farmers to gain greater control over variability in pasture-based dairy systems and improve the efficiency of resource use for profit and environmental outcomes
About Zitterbewegung and electron structure
We start from the spinning electron theory by Barut and Zanghi, which has
been recently translated into the Clifford algebra language. We "complete" such
a translation, first of all, by expressing in the Clifford formalism a
particular Barut-Zanghi (BZ) solution, which refers (at the classical limit) to
an internal helical motion with a time-like speed [and is here shown to
originate from the superposition of positive and negative frequency solutions
of the Dirac equation]. Then, we show how to construct solutions of the Dirac
equation describing helical motions with light-like speed, which meet very well
the standard interpretation of the velocity operator in the Dirac equation
theory (and agree with the solution proposed by Hestenes, on the basis
--however-- of ad-hoc assumptions that are unnecessary in the present
approach). The above results appear to support the conjecture that the
Zitterbewegung motion (a helical motion, at the classical limit) is responsible
for the electron spin.Comment: LaTeX; 11 pages; this is a corrected version of work appeared partly
in Phys. Lett. B318 (1993) 623 and partly in "Particles, Gravity and
Space-Time" (ed.by P.I.Pronin & G.A.Sardanashvily; World Scient., Singapore,
1996), p.34
Coherent states for Hopf algebras
Families of Perelomov coherent states are defined axiomatically in the
context of unitary representations of Hopf algebras possessing a Haar integral.
A global geometric picture involving locally trivial noncommutative fibre
bundles is involved in the construction. A noncommutative resolution of
identity formula is proved in that setup. Examples come from quantum groups.Comment: 19 pages, uses kluwer.cls; the exposition much improved; an example
of deriving the resolution of identity via coherent states for SUq(2) added;
the result differs from the proposals in literatur
Quantum Magnetic Algebra and Magnetic Curvature
The symplectic geometry of the phase space associated with a charged particle
is determined by the addition of the Faraday 2-form to the standard structure
on the Euclidean phase space. In this paper we describe the corresponding
algebra of Weyl-symmetrized functions in coordinate and momentum operators
satisfying nonlinear commutation relations. The multiplication in this algebra
generates an associative product of functions on the phase space. This product
is given by an integral kernel whose phase is the symplectic area of a
groupoid-consistent membrane. A symplectic phase space connection with
non-trivial curvature is extracted from the magnetic reflections associated
with the Stratonovich quantizer. Zero and constant curvature cases are
considered as examples. The quantization with both static and time dependent
electromagnetic fields is obtained. The expansion of the product by the
deformation parameter, written in the covariant form, is compared with the
known deformation quantization formulas.Comment: 23 page
Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations
Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.Comment: 29 pages, part 1 of two papers, published versio
The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations
In the recent paper hep-th/0502076, it was argued that the open topological
B-model whose target space is a complex (2|4)-dimensional mini-supertwistor
space with D3- and D1-branes added corresponds to a super Yang-Mills theory in
three dimensions. Without the D1-branes, this topological B-model is equivalent
to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the
latter with a holomorphic BF-type theory, we describe a twistor correspondence
between this theory and a supersymmetric Bogomolny model on R^3. The connecting
link in this correspondence is a partially holomorphic Chern-Simons theory on a
Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the
mini-supertwistor space. Along the way of proving this twistor correspondence,
we review the necessary basic geometric notions and construct action
functionals for the involved theories. Furthermore, we discuss the geometric
aspect of a recently proposed deformation of the mini-supertwistor space, which
gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually,
we present solution generating techniques based on the developed twistorial
description together with some examples and comment briefly on a twistor
correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio
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