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Multiresolution Quantum Field Theory in Light-Front Coordinates

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Abstract

We analyse the use of wavelet transform in quantum field theory models written in light-front coordinates. In a recent paper (Phys. Rev. D 101: 096004 2020) Polyzou used x+ variable as ‘time’, and applied wavelet transform to the ‘spatial’ coordinates only. This makes the theory asymmetric with respect to space and time coordinates. In present paper we generalise the concept of continuous causal path, which is the basis of path integration, to the sequences of causally ordered spacetime regions, and present evaluation rules for Feynman path integrals over such sequences in terms of wavelet transform. Both the path integrals and the wavelet transform in our model are symmetric with respect to the light-front variables (x+,x−). The definition of a spacetime event in our generalization is very much like the definition of event in probability theory.

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Acknowledgements

The authors are thankful to Profs. J.-P. Gazeau, M.Hnatich, S.Mikhailov, M.Perel, and W.N.Polyzou for useful comments and references.

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Authors and Affiliations

  1. Space Research Institute RAS, Profsoyuznaya 84/32, Moscow, 117997, Russia

    Mikhail V. Altaisky

  2. National University of Science and Technology ‘MISIS’, Leninsky av. 4, Moscow, 119049, Russia

    Natalia E. Kaputkina

  3. Mahatma Gandhi University, Priyadarsini Hills, Kottayam, Kerala, 686560, India

    Robin Raj

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  1. Mikhail V. Altaisky
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  3. Robin Raj
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Correspondence to Mikhail V. Altaisky.

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Altaisky, M.V., Kaputkina, N.E. & Raj, R. Multiresolution Quantum Field Theory in Light-Front Coordinates. Int J Theor Phys 61, 46 (2022). https://doi.org/10.1007/s10773-022-05029-6

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