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Eisenhart lift and Randers–Finsler formulation for scalar field theory

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Abstract

We study scalar field theory as a generalization of point particle mechanics using the Polyakov action and demonstrate how to extend Lorentzian and Riemannian Eisenhart lifts to the theory in a similar manner. Then, we explore extension of the Randers–Finsler formulation and its principles to the Nambu–Goto action and describe a Jacobi Lagrangian for it.

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Acknowledgements

We wish to acknowledge G. W. Gibbons, M. Cariglia and Joydeep Chakravarty for various discussions and support, P. Horvathy, K. Morand, A. Galajinsky and an anonymous reviewer for supportive comments and P. Mukhopadhay for introducing us to scalar field theory, all of which were instrumental in the preparation of this article.

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Authors and Affiliations

  1. International Centre for Theoretical Sciences, No. 151, Shivakote, Hesaraghatta Hobli, Bengaluru, Karnataka, 560089, India

    Sumanto Chanda

  2. Department of Mathematics, Khalifa University, Zone 1, Abu Dhabi, United Arab Emirates

    Partha Guha

Authors
  1. Sumanto Chanda
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  2. Partha Guha
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Correspondence to Sumanto Chanda.

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Chanda, S., Guha, P. Eisenhart lift and Randers–Finsler formulation for scalar field theory. Eur. Phys. J. Plus 136, 66 (2021). https://doi.org/10.1140/epjp/s13360-020-01066-4

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-01066-4

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