Abstract
The content of two additional Ward identities exhibited by the U(1) Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs particle and the massive vector boson is introduced in the theory from the beginning. Among the results obtained from the above mentioned Ward identities, we underline a new exact relationship between the stationary condition for the vacuum energy, the vanishing of the tadpoles and the vacuum expectation value of the gauge invariant scalar operator. We also present a characterization of the two-point correlation function of the composite operator corresponding to the vector boson in terms of the two-point function of the elementary gauge fields. Finally, a discussion on the connection between the cartesian and the polar parametrization of the complex scalar field is presented in the light of the Equivalence Theorem. The latter can in the current case be understood in the language of a constrained cohomology, which also allows to rewrite the action in terms of the aforementioned gauge invariant operators. We also comment on the diminished role of the global U(1) symmetry and its breaking.
Highlights
Following the standard quantum field theory setup [10], in order to study the correlation functions of the local composite operators (O(x), Vμ(x)) one has to introduce them in the starting action by means of a suitable pair of external sources (J(x), Ωμ(x))
Let us point out that this global symmetry is manifestly preserved by the Landau gauge, being broken in the Rξ gauge by unphysical BRST exact terms which can be kept under control to all orders by means of the introduction of a suitable set of BRST doublets of external sources, see the extensive analysis worked out in [11, 12]
We present an account of the connection between the Higgs model expressed in cartesian coordinates and polar coordinates4 in the light of the Equivalence Theorem [21,22,23,24], a general result in quantum field theory stating that field redefinitions have no effects on physical observable quantities like the S-matrix amplitudes
Summary
In previous work [2], we introduced a resummation scheme for the connected diagrammatic contributions to the correlation function of the composite operators. Given the higherdimensionality of e.g. the operator Vμ, the UV tail of the corresponding propagator is blowing up ∼ p4 (up to logs), impairing a resummation of the full set of diagrams into an improved tree level propagator, as the tree level contribution to VμVν T is given by m4 4e2. The question to be answered here is whether the resummation strategy of [2], which can be immediately generalized to the non-Abelien case [35], is compatible with the Ward identity (6.13), since in contrast with Vμ(p)Vν(−p) T , the loop corrections to Aμ(p)Aν(−p) T were fully resummed in [2]. Returning to the Ward identity (6.23), the same resummation procedure can be applied to its r.h.s., leading to full compatibility with the l.h.s. Notice that due to the presence of an overall (p2 + m2) in front of the third term, this term will only contribute to π1(p) and we see that π0(p) = ΠTAA(p), thereby immediately confirming that the pole mass is identical to that of Aμ(p)Aν(−p) T
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
