We can see the definition of quantum anomaly in terms of Lagrangian path integral formulation. What is the definition of quantum anomaly in terms of Hamiltonian operator approach or even more directly in terms of wave functions? What are the characteristics of anomalous Hamiltonians or wave functions?

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    $\begingroup$ A quick google search turned up this article: link.springer.com/article/10.1007%2FBF01466595. Sadly, only a preview is freely available, which is a shame since it appears exactly what you're looking for. $\endgroup$ – David H Apr 6 '14 at 9:41
  • $\begingroup$ Thanks David. I found that paper and I need to buy it. I may contact our librarian next week. $\endgroup$ – hehuan0430 Apr 6 '14 at 18:35
  • $\begingroup$ By quantum anomaly, we usually mean that a symmetry present in a classical theory (say, Gauss's Law) is not present after quantization. If you want to see a specific example in 2-d, have a look at chapter 4 of circle.ubc.ca/bitstream/handle/2429/29272/UBC_1989_A1%20R62.pdf where one can see how an anomaly manifest itself when one looks at commutation relations of operators in the Hamiltonian formalism. $\endgroup$ – André Apr 10 '14 at 20:11

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