Talk:Lattice quantum field theory
Reviewer B
Comments on "Lattice quantum field theory" by Gernot Munster
- p.6: The Euclidean path integral sort of drops out of the blue sky. A reference to the book "Quantum Physics" by Glimm and Jaffe might be helpful.
- Somewhere in the Section "Euclidean Field Theory" a reference to the theorem of Osterwalder and Schrader, providing the theoretical basis for the Euclidean method, would be in order.
- p.9: The introduction of the lattice constant a is somewhat misleading. It is certainly not a parameter to be inserted in a computer program for an evaluation (e.g. via Monte Carlo) of the path integral. It should be made clear that it is a derived quantity determined by the dynamics. This is actually explained later, in the Section "Continuum Limit", but it would be appropriate to mention it right away.
- p. 16: I think it is worth mentioning that the strong coupling expansion has a finite radius of convergence, whereas perturbation theory is expected to be divergent and at best asymptotic.
- pp. 18-19: It would be important to bring out the difference between `scaling' and `asymptotic scaling' (Eq. (5)). It should further be made clear that the former, essential for the existence of a continuum limit, is numerically quite well established, wheras the latter has (to the best of my knowledge) never been confirmed.
Moreover: Greens --> Green's, analytical --> analytic, Brillouin zone --> first Brillouin zone.
Further comment (Dec. 3rd, 2010):
The reference to the Osterwalder-Schrader theorem should be
K.~Osterwalder and R.~Schrader, Commun.\ Math.\ Phys.\ {\bf 31} (1973) 83; Commun.\ Math.\ Phys.\ {\bf 42} (1975) 281.
It is important to cite both papers because the first one contains an error which is corrected in the second one.
Reviewer B (User:):
Further comment (Dec. 3rd, 2010): The reference to the Osterwalder-Schrader theorem should be
K.~Osterwalder and R.~Schrader, Commun.\ Math.\ Phys.\ {\bf 31} (1973) 83; Commun.\ Math.\ Phys.\ {\bf 42} (1975) 281.
It is important to cite both papers because the first one contains an error which is corrected in the second one.
