Mikio Nakahara. creator Mikio Nakahara. text Mathematics.-Topology.-Physics - Mathematics-Geometry. xxu Bristol, England ; New York : Taylor & Francis , ©2003 monographic eng

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xxii,573p. :24cm. 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. 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. / Mikio Nakahara. 516.36 NAK 9780750306065 International Book Distributors Flat No.-17 , Prakash Apartment , 5 Ansari Road, Daryaganj , New Delhi. 180404 20180418110300.0