GRK 52: Quantum Field Theory: Mathematical Structure and Applications to Elementary Particle and Solid State Physics

研究训练组的目的是将莱比锡传统的数学和理论物理相互作用中培养出来的量子场论的科学能力传给下一代，量子场论已成为现代物理学的一个重要课题。有三个研究领域：1)量子场论的数学结构（微分几何、代数、非交换几何、量子群和算子代数中一般概念的基础和物理相关方法的发展）。II A)基本粒子物理的量子场论（基本粒子和相互作用，包括引力，标准模型及其超对称扩展，其现象学方面和晶格近似，以及外部经典场构型）。II B)固体量子场论（固体，特殊的多粒子系统和量子统计方面，高温超导，强相关电子系统和量子磁体，相变和有限尺寸效应）。这些青年科学家在量子场论的整个领域，特别是在量子场论的数学和物理方法及其应用方面，都超越了他们的狭窄研究课题。特别是，数学基础研究与物理方法进步之间的相互关系，以及相对论性、非相对论性和面向计算机的量子场论之间的相互关系是非常重要的。

The aim of the research training group is to pass on to further generations the scientific competence, grown in Leipzig's traditional interplay of Mathematics and Theoretical Physics, on Quantum Field Theory which has become an important subject of modern Physics.There are three domains of research:I) Mathematical Structure of Quantum Field Theory (fundamentals of general concepts and development of physically relevant methods from Differential Geometry, Algebra, Non-commutative Geometry, Quantum Groups, and Operator Algebras).II A) Quantum Field Theory of Elementary Particle Physics (fundamental particles and interactions including gravitation, the Standard Model and its supersymmetric extensions, its phenomenological aspects and lattice approximations, and external classical field configurations).II B) Quantum Field Theory of Solids (solids, special many-particles systems and aspects of quantum statistics, high temperature superconduction, strongly correlated electron systems and quantum magnets, phase transitions and finite size effects).The junior scientists are qualified beyond their narrow research topic in the entire field of Quantum Field Theory, especially to its mathematical and physical methods and its applications. In particular, the interrelation between mathematical basic research and progress in physical methods as well as between relativistic, non-relativistic and computer-oriented Quantum Field Theory is of great importance.