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Hamiltonian formulation of the (1+1)-dimensional ϕ4 theory in a momentum-space Daubechies wavelet basis

Mrinmoy Basak1,*, Debsubhra Chakraborty1,†, Nilmani Mathur1,‡, and Raghunath Ratabole2,§

  • *Contact author: mrinmoy.263009@gmail.com
  • †Contact author: debsubhrachakraborty162@gmail.com
  • ‡Contact author: nilmani@theory.tifr.res.in
  • §Contact author: ratabole@goa.bits-pilani.ac.in
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Phys. Rev. D 113, 085021 – Published 27 April, 2026

DOI: https://doi.org/10.1103/74c7-y1gp

Abstract

We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework. In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution and translation indices, providing a natural nonperturbative truncation of both infrared and ultraviolet truncation of quantum field theories. As an application, we compute the energy spectra of a free scalar field theory and the interacting 1+1-dimensional ϕ4 theory. This approach successfully reproduces the well-known strong-coupling phase transition in the m2>0 regime. Our results indicate that with increasing resolution, the extracted critical coupling can approach toward its expected value, providing numerical evidence for the plausibility of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.

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Phys. Rev. D 113, 085021– Published 27 April, 2026
  • Received 9 February 2026
  • Accepted 1 April 2026
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