Equivalence theorems and point transformations in field theory

Field redefinitions in effective theories at higher orders

“…We have grouped the terms by their origin, rather than by the powers of M −2 . The terms in the first two lines of this equation arise from the redefinition of L SM , the ones in the third and fourth lines come from L (6) eff and the fifth line is just L We observe that removing the dimension-6 term proportional to D 2 φ complicates the Lagrangian significantly in several ways. First, there are more operators.…”

“…3 This property of quantum field theory is sometimes known as the equivalence theorem (not to be confused with the equivalence theorem in the Higgs mechanism). Different versions of this theorem, with different assumptions and in different contexts, have been proved and discussed in the literature [4][5][6][7][8][9][10]. Here we have in mind the application of the effective field theory to the scattering of particles.…”

“…6) for some h α . For a non-trivial action S and a generic f α , there is no solution to this equation, since the first and second derivatives give a non-homogeneous result when acting on terms in S with different number of fields.…”

Equivalence theorem in effective theories

“…The equivalence theorem (ET) has been known since the early 1960s [1][2][3][4][5][6] and has been considered by different authors from various points of view (see, e.g., [7][8][9][10][11][12][13]). However, many practical aspects of this theorem remain unclear.…”

“…In papers [15][16][17] it is shown that such a content results from additional physical and mathematical requirements: localizability, summability, uniformity, and reasonable asymptotic behavior of amplitudes. 3 See, however, the note in the last paragraph of Sec. V Here it is pertinent to note that the term ''perturbative equivalence'' makes no sense until the perturbation schemes for both theories are specified.…”