TY - BOOK AU - Mikio Nakahara. AU - Mikio Nakahara. TI - Geometry, topology, and physics T2 - Graduate student series in physics SN - 9780750306065 U1 - 516.36 NAK PY - 2003/// CY - Bristol, England ; New York PB - : Taylor & Francis KW - Mathematics KW - Topology KW - Physics - Mathematics KW - Geometry N1 - Quantum Physics -- Analytical mechanics -- Newtonian mechanics -- Lagrangian formalism -- Hamiltonian formalism -- Canonical quantization -- Hilbert space, bras and kets -- Axioms of canonical quantization -- Heisenberg equation, Heisenberg picture and Schrodinger picture -- Wavefunction -- Harmonic oscillator -- Path integral quantization of a Bose particle -- Path integral quantization -- Imaginary time and partition function -- Time-ordered product and generating functional -- Harmonic oscillator -- Transition amplitude -- Partition function -- Path integral quantization of a Fermi particle -- Fermionic harmonic oscillator -- Calculus of Grassmann numbers -- Differentiation -- Integration -- Delta-function -- Gaussian integral -- Functional derivative -- Complex conjugation -- Coherent states and completeness relation -- Partition function of a fermionic oscillator -- Quantization of a scalar field -- Free scalar field -- Interacting scalar field -- Quantization of a Dirac field -- Gauge theories -- Abelian gauge theories -- Non-Abelian gauge theories -- Higgs fields -- Magnetic monopoles -- Dirac monopole -- The Wu-Yang monopole -- Charge quantization -- Instantons -- The (anti- )self-dual solution -- Mathematical Preliminaries -- Equivalence relation and equivalence class -- Vector spaces -- Vectors and vector spaces -- Linear maps, images and kernels -- Dual vector space -- Inner product and adjoint -- Tensors -- Topological spaces -- Continuous maps -- Neighbourhoods and Hausdorff spaces -- Closed set N2 - This book introduces several current mathematical methods to postgraduate students of theoretical physics. This is achieved by presenting applications of the mathematics to physics, high-energy physics, general relativity and condensed matter physics ER -