Path Integral and functional methods in quantum field theory


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Path integral method is an important formal development in quantum mechanics. The first half of the course should be useful for any student of quantum mechanics, providing deeper insights into the theory. The second half of the course discusses path integral method in its functional form applied to space-time fields and brings out connection of quantised fields to elementary particles.
Quantum theory is increasingly a part of many practical developments, from materials science and nanotechnology to quantum computation. Deeper insights and exposure to novel computational approaches in it will be of use to a wide audience. Specifically within theories of elementary particles, a grasp of this method is a stepping stone to more advanced topics such as String Theory.
INTENDED AUDIENCE: Students of final year of B.Sc.(Physics/Mathematics), final year of B.Tech, M.Sc and PhD students.PREREQUISITES: Relativistic Quantum Mechanics and free scalar field quantisation



Week 1: Quantum Theory Fundamental Quantisation and Path Integral Formulation.Week 2: Path Integral Formulation and Correlation Functions.Week 3: Generating Functional, Forced Harmonic Oscillator and Generating Function in Field Theory.Week 4: Effective Potential.Week 5: Asymptotic Theory, Asymptotic Condition Kallen-Lehmann Representation.Week 6: Gauge Invariance.Week 7: Yang Mills Theory and Yang Mills Theory Constraint Dynamics.Week 8: Gauge Fixing and Faddeev Popov Ghosts and Vacuum topology of Yang-mills Theories.