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ward identities under the frame transformations in curved space-time

Communications in Theoretical Physics 2024年第9期76卷 107-117页

作者： Susobhan Mandal Department of Physics Indian Institute of Technology BombayMumbai 400076India

Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity,as they are used to build feasible models for cosmic *** theories can be formulated both in the Jordan and Einstein frame,which are related by a Weyl transformation with a field transformation,known together as a frame *** theories formulated in the above two frames are often considered to be equivalent from the point of view of classical ***,this is no longer true from the quantum field theoretical *** the present article,we show that the ward identities derived in the above two frames are not connected through the frame *** shows that the quantum field theories formulated in these two frames are not equivalent to each ***,this inequivalence is also shown by comparing the effective actions derived in these two frames.

关键词： ward identities frame transformations curved spacetime

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Can Really Regularized Amplitudes Be Obtained as Consistent with Their Expected Symmetry Properties?

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Journal of Modern Physics 2018年第6期9卷 1153-1178页

作者： Orimar Antonio Battistel Gilson Dallabona Marcus Vinicios Fonseca Luciana Ebani Departamento de Física Universidade Federal de Santa MariaSanta MariaBrazil Departamento de Física Universidade Federal de LavrasLavrasBrazil Instituto Federal Farroupilha Sao Vicente do SulBrazil Centro Brasileiro de Pesquisas Física Rio de JaneiroBrazil

Through a very detailed investigation involving a set of simple perturbative amplitudes we show that the answer for the question put in the title of the present work is: undoubtedly NO! We are not restricting the sentence to the amplitudes which are considered as anomalous. The referred investigation is performed by using a procedure alternative to the traditional regularization methods. In the context of such a strategy the amplitudes are not modified in intermediary steps of the calculation, like traditional regularization procedures do, and only the validity of the linearity in the integration operation is assumed in the operations made in Feynman integrals typical of the perturbative calculations. The central point of the investigation is the question related to the consistent interpretation of the amplitudes. For these purposes, in all amplitudes having power counting indicating the possibility of divergences, the relations among Green functions, ward identities and low energy limits are analyzed, in a model having different species of massive 1/2 spin fermions coupled to spin 0 and 1 (even and odd parity) boson fields, formulated in a space-time dimension D=1+1. We show that the maintenance of the linearity in operations involving Feynman integrals excludes the possibility of an anomalous term in the ward identity relating the axial-vector and the pseudo-scalar-vector two point functions amplitudes. In addition, we show that it is not possible the maintenance of ward identities and low energy limits in a consistent way if the amplitudes of the perturbative calculations are quantities to be regularized, just because there is no regularization method which is capable to give acceptable results for the divergent objects present in the calculations. This conclusion includes the Dimensional Regularization method which cannot give unique results if the linearity and the symmetric integration are simultaneously required in Feynman integrals. The qualitative conclusio

关键词： Perturbative Calculations Anomalies ward identities Consistency

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