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Unformatted text preview: Homework Set No. 3, Physics 880.08 Deadline Wednesday, May 18, 2011 1. a. (5 pts) By explicitly expanding the exponentials on the left-hand-side and carrying out the Grassmann integrals show that the following relation holds integraldisplay d 1 d 1 d 2 d 2 exp bracketleftBigg- summationdisplay i,j a ij i j bracketrightBigg exp bracketleftBigg summationdisplay k ( k k + k k ) bracketrightBigg = (det A ) exp bracketleftBigg summationdisplay i,j i A- 1 ij j bracketrightBigg where i and j are Grassmann variables, and A is a 2 2 Hermitean matrix with elements a ij . b (5 pts) Show that- i F = F = F i F = F = F for the function F = exp bracketleftbig i ( + ) bracketrightbig . Here and are Grassmann variables. 2. Nature of the perturbation series. Consider a zero-dimensional field theory defined by the path integral I ( m, ) = integraldisplay-...
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