Lecture notes on path-integrals, suitable for an undergraduate course with prerequisites such as: Classical Mechanics, Electromagnetism and Quantum Mechanics. The aim is to provide the reader, who is familiar with the major concepts of Solid State Physics, to study these topics couched in the language of path integrals. We endeavor to keep the formalism to the bare minimum.
Keywords
Path-integrals; Quantum Field Theory; Solid State Models
The integral is discretized into a sum. Summing over all paths means adding the contribution of possible lines with the proper weight. Here we show only two paths for discretized time . The dynamical variable is also discretized .
Wick rotation of the blue contour C, running along the real -axis, into the red contour C’, running along the imaginary -axis, without crossing the poles. These are shown as blobs, whose distance to the vertical axis is .
: second order contribution to the trace. The thin lines stand for the propagators . Notice momentum conservation at the vertices.
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