Primer of Analytical Mechanics

Franco Strocchi graduated at Pisa University and at Scuola Normale Superiore, Pisa, and then has been Research Fellow of the National Institute of Nuclear Physics (INFN) and Lecturer at Pisa University and at Scuola Normale Superiore. Later, he has been Full Professor of Theoretical Physics at the International School for Advanced Studies in Trieste (SISSA) and Professor of Theoretical Physics at Scuola Normale Superiore, Pisa. He is the author of more than one hundreds of papers on theoretical and mathematical physics and of the following books: Elements of Quantum Mechanics of Infinite Systems (World Scientific, 1985); Selected Topics on the General Properties of Quantum Field theory, (World Scientific, 1993); Symmetry Breaking (Springer, 2005, 2008); An Introduction to the Mathematical Structure of Quantum Mechanics (World Scientific, 2005, 2008, 2010); An Introduction to Non-Perturbative Foundations of Quantum Field Theory (Oxford University Press, 2013, 2016); Gauge Invariance and Weyl-polymer Quantization (Springer, 2016).He has been Research Associate and Visiting Professor at Princeton University (USA), Visting Scientist at Cern, Visiting Schroedinger Professor at the University of Vienna.

• Preface.- 1 Difficulties of Cartesian Newtonian Mechanics.- 1.1 Constraint forces.- 1.2 Non-inertial frames and fictitious forces.- 2 Lagrange equations.- 2.1 Degrees of freedom and Lagrangian coordinates.- 2.2 Lagrangian form of Newton's equations.- 2.3 Lagrange equations.- 2.4 Lagrange equations at work. Examples.- 2.5 Generalized potential.- 2.6 Larmor theorem.- 2.7 Physical meaning of Lagrange equations; conjugate momenta.- 2.8 Cyclic variables, symmetries and conserved conjugate momenta.- 2.9 Non-uniqueness of the Lagrangian.- 3 Hamilton equations.- 3.1 Energy conservation.- 3.2 Hamilton equations.- 3.3 Coordinate transformations and Hamilton equations.- 3.4 Canonical transformations.- 4 Poisson brackets and canonical structure.- 4.1 Constants of motion identified by.- Poisson brackets.- 4.2 General properties of Poisson brackets.- 4.3 Canonical structure.- 4.4 Invariance of Poisson brackets under canonical transformations.- 5 Generation of canonical transformations.- 5.1 Alternative characterization of canonical transformations.- 5.2 Extended canonical transformations.- 5.3 Generators of continuous groups of canonical transformations.- 5.4 Symmetries and conservation laws. Noether theorem.- 6 Small oscillations.- 6.1 Equilibrium configurations. Stability.- 6.2 Small oscillations.- 7 The common Poisson algebra of classical and quantum mechanics.- 7.1 Dirac Poisson algebra.- 7.2 A common Poisson algebra of classical and quantum mechanics.- Index.