A novel Hamiltonian formulation of $1+1$ dimensional $φ^4$ theory in Daubechies wavelet basis: momentum space analysis

• URL: http://arxiv.org/abs/2601.22953v1
• Date: Fri, 30 Jan 2026 13:16:00 GMT
• Title: A novel Hamiltonian formulation of $1+1$ dimensional $φ^4$ theory in Daubechies wavelet basis: momentum space analysis
• Authors: Mrinmoy Basak,
• Abstract summary: We employ the wavelet formalism of quantum field theory to study field theories in the nonperturbative Hamiltonian framework.<n>We consider the $4$ theory and demonstrate the emergence of the well-known nonperturbative strong-coupling phase transition in the $m2>0$ sector.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: 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.

Related papers

• Hamiltonian formulation of the $1+1$-dimensional $φ^4$ theory in a momentum-space Daubechies wavelet basis [0.0]
  We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework.<n>In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution and translation indices.
  arXiv  Detail & Related papers  (2026-01-26T12:57:10Z)
• Bound polariton states in the Dicke-Ising model [41.94295877935867]
  We present a study of hybrid light-matter excitations in cavity QED materials.<n>We derive the exact excitations of the system in the thermodynamic limit.
  arXiv  Detail & Related papers  (2024-06-17T18:00:01Z)
• Entanglement in $(1+1)$-dimensional Free Scalar Field Theory: Tiptoeing between Continuum and Discrete Formulations [0.0]
  We show how the formalism developed for the discretized theory can be utilized in order to obtain results in the continuous theory.<n>In a specific coordinate system, the modular Hamiltonian assumes the form of a free field Hamiltonian on the Rindler wedge.
  arXiv  Detail & Related papers  (2024-06-16T18:00:42Z)
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model [44.84660857803376]
  We study level pairings in the many-body spectrum of the random-field Floquet quantum Ising model. The robustness of $pi$ pairings against longitudinal disorder may be useful for quantum information processing.
  arXiv  Detail & Related papers  (2024-01-09T20:37:48Z)
• Local quenches in fracton field theory: Lieb-Robinson bound, non-causal dynamics and fractal excitation patterns [37.69303106863453]
  We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension.
  arXiv  Detail & Related papers  (2023-10-17T12:21:15Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Matter relative to quantum hypersurfaces [44.99833362998488]
  We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
  arXiv  Detail & Related papers  (2023-08-24T16:39:00Z)
• String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory [0.0]
  We study the Hamiltonian lattice Yang-Mills theory based on spin networks. We study quantum scars in a nonabelian gauge theory.
  arXiv  Detail & Related papers  (2023-05-10T07:45:43Z)
• Qubitization strategies for bosonic field theories [0.0]
  We show two different truncations that preserve the symmetries of the 1+1-dimensional $O(3)$ non-linear $sigma$-model. We provide evidence that the angular-momentum truncation fails to reproduce the $sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.
  arXiv  Detail & Related papers  (2022-08-31T20:30:42Z)
• Light-shift induced behaviors observed in momentum-space quantum walks [47.187609203210705]
  We present a theoretical model which proves that the coherent dynamics of the spinor condensate is sufficient to explain the experimental data. Our numerical findings are supported by an analytical prediction for the momentum distributions in the limit of zero-temperature condensates.
  arXiv  Detail & Related papers  (2022-05-16T14:50:05Z)
• Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory [0.0]
  In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) Our model relies on a relativistic phase harmony' condition locking the phases of the solitonic particle and the guiding wave.
  arXiv  Detail & Related papers  (2022-05-10T07:11:54Z)
• Dimerization of many-body subradiant states in waveguide quantum electrodynamics [137.6408511310322]
  We study theoretically subradiant states in the array of atoms coupled to photons propagating in a one-dimensional waveguide. We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization. We reveal the breakdown of fermionized subradiant states with increase of $f$ with emergence of short-ranged dimerized antiferromagnetic correlations.
  arXiv  Detail & Related papers  (2021-06-17T12:17:04Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.