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

研究培训小组的目的是将在莱比锡传统的数学和理论物理相互作用中培养出来的关于量子场论的科学能力传授给下一代人，量子场论已成为现代物理学的一个重要学科。研究有三个领域：i)量子场论的数学结构(一般概念的基础和物理相关方法的发展，从微分几何、代数、非对易几何、量子群和算符代数)。ii)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、其唯象方面和晶格近似)固体的量子场论(固体、特殊的多粒子系统和量子统计、高温超导、强关联电子系统和量子磁铁、相变和有限尺寸效应)。初级科学家在整个量子场论领域的狭隘研究课题之外，特别是它的数学和物理方法及其应用，是合格的。特别是，数学基础研究与物理方法的进步之间的相互关系，以及相对论、非相对论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.