**"LQP Crossroads" is an international forum**

**for information exchange among scientists**

**working on mathematical, conceptual, and constructive problems**

**in local relativistic quantum physics (LQP).**

LQP is an approach to quantum field theory which complements other modern developments in relativistic quantum field theory. It is particularly powerful for structural analysis but has also proven to be useful in the rigorous treatment of models.

Its setting is designed to describe a large variety of physical systems ranging from the constituents of elementary particles to relativistic bulk matter. It is based on the fundamental principles underlying Quantum Theory and Relativity - most prominently the statistical interpretation of QT, the spacetime localizability of physical observables, Einstein causality, and relativistic invariance.

The LQP approach emphasizes that the physical content of a quantum field theory is intrinsically determined by the algebraic relations between its local observables. One of its principal aims is therefore the unambiguous characterization, classification, and physical interpretation of local quantum theories in terms of the algebras of observables.

The following list of topics, being presently in the center of interest of the Göttingen LQP group, might give an idea of the broad spectrum of questions within the context of LQP:

- Construction and classification of local quantum field theories using recent progress in modular theory; characterization in terms of phase space properties.
- Development of algebraic concepts and analytical methods for discussing the particle and symmetry aspects of local gauge theories at small and large spacetime scales (ultra- and infraparticles).
- Consolidation of the mathematical treatment and physical interpretation of relativistic (non-) equilibrium states.
- Extension of the framework to include quantum gravitation with methods of microlocal analysis and non-commutative geometry.
- Analysis of low-dimensional quantum field theory models.
- Implementation of "holographic" relations between quantum field theories in different dimensions.

To treat these problems, methods from several disciplines in mathematics and physics have to be combined and further developed. This requires and stimulates an exchange between groups with expertise in quite different areas, ranging from differential geometry, functional analysis, the theory of operator algebras and non-commutative geometry on the mathematical side to general relativity, the foundations of quantum theory, quantum statistical mechanics and quantum field theory (including its modern ramifications) in physics. LQP also arouses the interest of philosophers of science who contribute to its conceptual foundations.

The results of these combined efforts are expected to demonstrate the potential of the theory and to provide vital impulses to future applications.