Hamiltonian formulation of the $1+1$-dimensional $ϕ^4$ theory in a momentum-space Daubechies wavelet basis
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910168188452864 |
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| author | Basak, Mrinmoy Chakraborty, Debsubhra Mathur, Nilmani Ratabole, Raghunath |
| author_facet | Basak, Mrinmoy Chakraborty, Debsubhra Mathur, Nilmani Ratabole, Raghunath |
| contents | 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 $ϕ^4$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian formulation of the $1+1$-dimensional $ϕ^4$ theory in a momentum-space Daubechies wavelet basis Basak, Mrinmoy Chakraborty, Debsubhra Mathur, Nilmani Ratabole, Raghunath High Energy Physics - Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Quantum Physics 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 $ϕ^4$ 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. |
| title | Hamiltonian formulation of the $1+1$-dimensional $ϕ^4$ theory in a momentum-space Daubechies wavelet basis |
| topic | High Energy Physics - Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2601.18449 |