Abstract
Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional renormalization to verify the existence of transverse anomalies to one-loop order and any loop order, respectively. The arbitrariness of coefficients of transverse anomalies is revealed, and a way out is also proposed after relating transverse anomalies to Schwinger terms and comparing symmetry and non-symmetry anomalies. Papers that claim the non-existence of transverse anomalies are reviewed to find anomalies hidden in their approaches. The role played by transverse anomalies is discussed.
Highlights
There are always surprises in common quantization procedures, let alone the quantization of relativistic fields, which is highly entangled with infinite degrees of freedom, with various divergences and anomalies revealing the power of quantum laws
We focus on the Abelian case only, while the non-Abelian generalization is presented in Appendix A [see Eq (A3)] but is to be investigated in detail elsewhere
The (d − 4) term the authors discovered is a spurious anomaly corresponding to corrections of coefficients of terms existing in the tWTI, such as N1⁄2εμνρσψγσγ5iDρψ, because they only examined one-loop diagrams with two external fermion legs and did not note the crucial diagram with one external photon legs that generates transverse anomalies
Summary
There are always surprises in common quantization procedures, let alone the quantization of relativistic fields, which is highly entangled with infinite degrees of freedom, with various divergences and anomalies revealing the power of quantum laws. According to the above argument, as long as equations of motion are used in derivations of a WTI and the time-ordered product definition of operators is taken, an anomaly in the form of singular contact terms like tr1⁄2γ5δ4ðx − xÞ and tr1⁄21δ4ðx − xÞ may appear.. According to the above argument, as long as equations of motion are used in derivations of a WTI and the time-ordered product definition of operators is taken, an anomaly in the form of singular contact terms like tr1⁄2γ5δ4ðx − xÞ and tr1⁄21δ4ðx − xÞ may appear.5 This helps us greatly to anticipate possible anomalies in new WTIs—not necessarily one that stands for some symmetry—before resorting to rigorous all-order methods, such as dimensional renormalization.
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
