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Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate

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Abstract

The success of the S-matrix in quantum field theory in Minkowski spacetime naturally demands the extension of the construction of the S-matrix in a general curved spacetime in a covariant manner. However, it is well-known that a global description of the S-matrix may not exist in an arbitrary curved spacetime. Here, we give a local construction of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinates which mimics the methods, generally used in Minkowski spacetime. Using this construction, the scattering amplitudes and cross sections of some scattering processes are computed in a generic curved spacetime. Further, it is also shown that these observables can be used to probe features of curved spacetime as these local observables carry curvature-dependent corrections. Moreover, the compatibility of the local construction of the S-matrix with the spacetime symmetries is also discussed in detail.

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Acknowledgements

SM wants to thank IISER Kolkata for supporting this work through a doctoral fellowship. He also wants to thank IIT-Jodhpur for their kind hospitality during his stay there, where a part of the work and relevant discussions were done.

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Authors and Affiliations

  1. Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741 246, WB, India

    Susobhan Mandal

  2. Indian Institute of Technology Jodhpur, Jodhpur, India

    Subhashish Banerjee

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  1. Susobhan Mandal
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  2. Subhashish Banerjee
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Correspondence to Susobhan Mandal.

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Mandal, S., Banerjee, S. Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate. Eur. Phys. J. Plus 136, 1064 (2021). https://doi.org/10.1140/epjp/s13360-021-02037-z

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