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arXiv · 2601.18449

Hamiltonian formulation of the $1+1$-dimensional $\phi^4$ theory in a momentum-space Daubechies wavelet basis

Mrinmoy Basak·Debsubhra Chakraborty·Nilmani Mathur·Raghunath Ratabole
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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 $\phi^4$ theory. This approach successfully reproduces the well-known strong-coupling phase transition in the $m^2 > 0$ regime. We find that the extracted critical coupling systematically converges toward its established value as the momentum resolution is increased, demonstrating the effectiveness of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.

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Mrinmoy Basak, Debsubhra Chakraborty, Nilmani Mathur, Raghunath Ratabole. 2026-01-26. Hamiltonian formulation of the $1+1$-dimensional $\phi^4$ theory in a momentum-space Daubechies wavelet basis. https://doi.org/10.1103/74c7-y1gp

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