Introduction to path integrals - McGill University

1 Introduction to path integralsv. January 22, 2006 Phys 719 - M. HilkeCONTENT Classical stochastic dynamics Brownian motion (random walk) quantum dynamics Free particle Particle in a potential Driven harmonic oscillator Semiclassical approximation Statistical description (imaginary time) quantum dissipative systemsINTRODUCTIONPath integrals are used in a variety of fields, includingstochastic dynamics, polymer physics, protein folding,field theories, quantum mechanics, quantum field theo-ries, quantum gravity and string theory. The basic ideais to sum up all contributing paths. Here we will overviewthe technique be starting on classical dynamics, in par-ticular, the random walk problem before we discuss thequantum case by looking at a particle in a potential, andfinish with an example of a quantum dissipative system,where this technique bares all its STOCHASTIC DYNAMICSThe classical equation of motion for a particle i

quantum computing. On the other hand, in many solid state systems, the envi-ronmental coupling can be so strong that weak coupling theories are no longer valid. This is the regime where the path integral approach has proven to be very useful. It would be beyond the scope of this chapter even to attempt to give a com-

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