A novel Hamiltonian formulation of $1+1$ dimensional $ϕ^4$ theory in Daubechies wavelet basis: momentum space analysis
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908800332595200 |
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| author | Basak, Mrinmoy |
| author_facet | Basak, Mrinmoy |
| contents | We employ the wavelet formalism of quantum field theory to study field theories in the nonperturbative Hamiltonian framework. Specifically, we make use of Daubechies wavelets in momentum space. These basis elements are characterised by a resolution and a translation index that provides for a natural nonperturbative infrared and ultraviolet truncation of the quantum field theory. As an application, we consider the $ϕ^4$ theory and demonstrate the emergence of the well-known nonperturbative strong-coupling phase transition in the $m^2>0$ sector. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A novel Hamiltonian formulation of $1+1$ dimensional $ϕ^4$ theory in Daubechies wavelet basis: momentum space analysis Basak, Mrinmoy High Energy Physics - Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Quantum Physics We employ the wavelet formalism of quantum field theory to study field theories in the nonperturbative Hamiltonian framework. Specifically, we make use of Daubechies wavelets in momentum space. These basis elements are characterised by a resolution and a translation index that provides for a natural nonperturbative infrared and ultraviolet truncation of the quantum field theory. As an application, we consider the $ϕ^4$ theory and demonstrate the emergence of the well-known nonperturbative strong-coupling phase transition in the $m^2>0$ sector. |
| title | A novel Hamiltonian formulation of $1+1$ dimensional $ϕ^4$ theory in Daubechies wavelet basis: momentum space analysis |
| topic | High Energy Physics - Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2601.22953 |