Exact phase space functional for two-body systems

The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently be obtained by minimizing the ground-state energy.Comment: Latex, 12 page

Quasi-pinning and entanglement in the lithium isoelectronic series

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank-eight approximation we find well-defined families of saturation conditions.Comment: 22 pages, 6 figures, minor changes, references adde

From geometric quantization to Moyal quantization

We show how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by ``doubling'' the phase space.Comment: 7 two-column pages, RevTeX, UCR--FM--03--9

Ensuring locality in QFT via string-local fields

String-local fields constitute a relatively new tool for solving quantum field theory, stressing and embodying locality and positivity. We examine here their usefulness -- as well as some drawbacks. Starting from just the physical masses and charges of the known particles, and bringing string independence in the Bogoliubov-Epstein-Glaser (BEG) theory framework, regarded as a means of discovery, one finds the allowed couplings of quantum fields associated to those particles, and thereby recovers all of the Standard Model (SM) without invoking theoretical prejudices. One of the outcomes is the requirement that the fields be governed by reductive Lie algebras. Another is the need for at least one scalar particle. Yet another is chirality of interactions mediated by massive particles. There is no room in this formulation for ``global'' gauge invariance as an a priori construct. Armed with this modern weapon, we reassess here a few classical and recent conundra. In particular, we examine new perspectives in cosmology from the adoption of string-local fields.Comment: Latex, 25 pages, no figures; v2: two references added. v3: minor corrections, adding 2 more references and a more informative title. These are (enlarged) lecture notes of the conference on "Higher Structures Emerging from Renormalisation", Erwin Schr\"odinger Institute, Vienna, November 202

Sums over paths adapted to quantum theory in phase space

The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further researchUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic

Phase-space representation for Galilean quantum particles of arbitrary spin

The phase-space approach to quantization is extended to incorporate spinning particles with Galilean symmetry. The appropriate phase space is the coadjoint orbit R^6 x S^2. From two basic principles, traciality and Galilean covariance, the Weyl symbol calculus is constructed. Then the Galilean-equivariant twisted products of functions on this phase space are identified.UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic

The significance of physiologically structured models for fish stock dynamics

The present working document contains the initial papers of a series whose ultimate purpose is to provide a realistic basis for a fresh appraisal of both the surplus production and the dynamic pool approaches to fishery yield analysis. The main idea is to tighten the conceptual framework of the "trinity" of recruitment, survival and growth, uncovering links among the three sectors by using recently developed physiologically structured models' methodology. There are good reasons to argue that this endeavour is appropriate and suitable for understanding tropical fisheries.UCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic