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

QED in external fields from the spin representation

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framework, depends on the choice of the ``right'' complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.Comment: 32 pages, Plain TeX, UCR-FM-01-9