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 $2\sum_{q<0} (2|q|-1)$ negative modes, where the sum goes over all negative eigenvalues $q$ of the non-Abelian charge $Q$. 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

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

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

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