BRST Extension of Geometric Quantization

Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost number zero recovers the constrained quantum states. Moreover this space of constrained states has a well-defined Hilbert space structure inherited from that of the original system. Treatments of these ideas in the Physics literature are more general but suffer from having states with infinite or zero "norms" and thus are not admissible as states. Also the BRST operator for many systems require regularization to be well-defined. In our more restricted context we show that our treatment does not suffer from any of these difficulties. This work was submitted for publication March 21,2006

Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

Effective Equations of Motion for Quantum Systems

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and geometrical picture is developed and shown to agree with effective action results, commonly derived through path integration, for perturbations around a harmonic oscillator ground state. The same methods are used to describe dynamical coherent states, which in turn provide means to compute quantum corrections to the symplectic structure of an effective system.Comment: 31 pages; v2: a new example, new reference

Multi-functional work journeys

For the vast majority of workers in the Kwinana Industrial Strip the private motor vehicle is largely preferred as the means of accomplishing the journey to and from work. This high level of private vehicle usage provides a greater opportunity for the journey to work to become multi-functional. This study reveals both the type and distribution of stops made by workers differs with age, gender, employment category, and residential postcode. From these findings it is suggested that, If any attempt is made to move people out of cars and onto any future public transport, the differing needs of the workforce must be addressed. That is, public transport transfer nodes must become focal points in that they provide services appropriate to worker needs

Quantum-Mechanical Dualities on the Torus

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.Comment: New examples added, some precisions mad

Extended diffeomorphism algebras in (quantum) gravitational physics

We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is characterized by the fundamental role assigned to a basic underlying symmetry. The developed mathematical formalism makes contact with the relevant gravitational notions by means of the addition of some extra structure. The specific manners in which this is accomplished, together with their corresponding physical interpretation, lead to different gravitational models. Distinct strategies are in fact briefly outlined, showing the versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure

Symplectic Cuts and Projection Quantization

The recently proposed projection quantization, which is a method to quantize particular subspaces of systems with known quantum theory, is shown to yield a genuine quantization in several cases. This may be inferred from exact results established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor

The design of a Space-borne multispectral canopy LiDAR to estimate global carbon stock and gross primary productivity

Understanding the dynamics of the global carbon cycle is one of the most challenging issues for the scientific community. The ability to measure the magnitude of terrestrial carbon sinks as well as monitoring the short and long term changes is vital for environmental decision making. Forests form a significant part of the terrestrial biosystem and understanding the global carbon cycle, Above Ground Biomass (AGB) and Gross Primary Productivity (GPP) are critical parameters. Current estimates of AGB and GPP are not adequate to support models of the global carbon cycle and more accurate estimates would improve predictions of the future and estimates of the likely behaviour of these sinks. Various vegetation indices have been proposed for the characterisation of forests including canopy height, canopy area, Normalised Difference Vegetation Index (NDVI) and Photochemical Reflectance Index (PRI). Both NDVI and PRI are obtained from a measure of reflectivity at specific wavelengths and have been estimated from passive measurements. The use of multi-spectral LiDAR to measure NDVI and PRI and their vertical distribution within the forest represents a significant improvement over current techniques. This paper describes an approach to the design of an advanced Multi-Spectral Canopy LiDAR, using four wavelengths for measuring the vertical profile of the canopy simultaneously. It is proposed that the instrument be placed on a satellite orbiting the Earth on a sun synchronous polar orbit to provide samples on a rectangular grid at an approximate separation of 1km with a suitable revisit frequency. The systems engineering concept design will be presented

Conformal Spinning Quantum Particles in Complex Minkowski Space as Constrained Nonlinear Sigma Models in U(2,2) and Born's Reciprocity

We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach (of nonlinear sigma-model type) and use a generalized Dirac method for the quantization of constrained systems, which resembles in some aspects the standard approach to quantizing coadjoint orbits of a group G. Physical wave functions, Haar measures, orthonormal basis and reproducing (Bergman) kernels are explicitly calculated in and holomorphic picture in these Cartan domains for both scalar and spinning quantum particles. Similarities and differences with other results in the literature are also discussed and an extension of Schwinger's Master Theorem is commented in connection with closure relations. An adaptation of the Born's Reciprocity Principle (BRP) to the conformal relativity, the replacement of space-time by the 8-dimensional conformal domain at short distances and the existence of a maximal acceleration are also put forward.Comment: 33 pages, no figures, LaTe