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Efficient wavelet-based Hamiltonian formulation of quantum field theories using flow equations

Mrinmoy Basak*, Debsubhra Chakraborty†, and Nilmani Mathur‡

  • *Contact author: mrinmoy.263009@gmail.com
  • †Contact author: debsubhra.chakraborty@tifr.res.in
  • ‡Contact author: nilmani@theory.tifr.res.in
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Phys. Rev. D 114, 014502 – Published 6 July, 2026

DOI: https://doi.org/10.1103/krjm-7h9c

Abstract

We propose an effective Hamiltonian formulation of quantum field theories using a Daubechies wavelet basis in position space. Combined with flow-equation methods of the similarity renormalization group (SRG), this approach provides an efficient framework for analyzing quantum field theories by reducing the dimensionality of the Hamiltonian and systematically decoupling degrees of freedom across scales. As an application, the free scalar field theory has been reformulated within this framework to calculate the low-lying energy spectrum of the theory. These basis elements are known to transform the free scalar field theory into a theory of coupled localized oscillators, each of which is labeled by a location and a resolution index. In this representation, the Hamiltonian is naturally organized into fixed-resolution blocks, alongside blocks associated with the interactions between different resolutions. To decouple the different resolution modes and obtain a block diagonalized Hamiltonian with each block associated with a fixed resolution, the flow equation approach of SRG is applied. Finally, we demonstrate that with increasing resolution, the low-energy spectrum can be extracted from the effective lowest-resolution block of the Hamiltonian, leading to a significant reduction in computational cost.

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Phys. Rev. D 114, 014502– Published 6 July, 2026
  • Received 21 April 2026
  • Accepted 29 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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