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该杂志发表了简短的通讯、研究和评论文章，致力于几何方法(包括交换和非交换微分几何、黎曼几何、芬斯勒几何、复几何、李群和李代数、束理论、同调和上同调、代数几何、全局分析、范畴理论、算子代数和拓扑)在数学和理论物理的所有领域的所有应用，包括:经典力学(拉格朗日、哈密顿、泊松公式);量子力学(也是半经典近似);ODE和PDE的哈密顿系统及其可积性物理变分结构与守恒定律系统与连续体热力学(亦称量子热力学与统计物理学);广义相对论和其他几何引力理论;粒子物理学的几何模型;超重力与超对称场理论经典场论和量子场论(亦称弯曲背景下的量子化);计理论;拓扑领域理论;弦、膜和扩展对象理论;全息术;量子引力、环量子引力和量子宇宙学;量子群的应用;量子计算;控制理论;几何的混乱。

This journal publishes short communications, research and review articles devoted to all applications of geometric methods (including commutative and non-commutative Differential Geometry, Riemannian Geometry, Finsler Geometry, Complex Geometry, Lie Groups and Lie Algebras, Bundle Theory, Homology an Cohomology, Algebraic Geometry, Global Analysis, Category Theory, Operator Algebra and Topology) in all fields of Mathematical and Theoretical Physics, including in particular: Classical Mechanics (Lagrangian, Hamiltonian, Poisson formulations); Quantum Mechanics (also semi-classical approximations); Hamiltonian Systems of ODE's and PDE's and Integrability; Variational Structures of Physics and Conservation Laws; Thermodynamics of Systems and Continua (also Quantum Thermodynamics and Statistical Physics); General Relativity and other Geometric Theories of Gravitation; geometric models for Particle Physics; Supergravity and Supersymmetric Field Theories; Classical and Quantum Field Theory (also quantization over curved backgrounds); Gauge Theories; Topological Field Theories; Strings, Branes and Extended Objects Theory; Holography; Quantum Gravity, Loop Quantum Gravity and Quantum Cosmology; applications of Quantum Groups; Quantum Computation; Control Theory; Geometry of Chaos.