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

• URL: http://arxiv.org/abs/2601.18449v2
• Date: Tue, 27 Jan 2026 19:14:36 GMT
• Title: Hamiltonian formulation of the $1+1$-dimensional $φ^4$ theory in a momentum-space Daubechies wavelet basis
• Authors: Mrinmoy Basak, Debsubhra Chakraborty, Nilmani Mathur, Raghunath Ratabole,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $φ^4$ 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.

Related papers

• A novel Hamiltonian formulation of $1+1$ dimensional $φ^4$ theory in Daubechies wavelet basis: momentum space analysis [0.0]
  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.
  arXiv  Detail & Related papers  (2026-01-30T13:16:00Z)
• Perturbative Input-Output Theory of Floquet Cavity Magnonics and Magnon Energy Shifts [0.0]
  We compute reflectance and transmittance spectra of cavity magnonics systems subject to a Floquet modulation.<n>We reproduce the characteristic sideband structure observed in recent Floquet cavity electromagnonics experiments.
  arXiv  Detail & Related papers  (2025-12-13T00:29:45Z)
• Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks [0.0]
  We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory.<n>We investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$.
  arXiv  Detail & Related papers  (2025-10-31T18:00:46Z)
• Inflationary power spectrum from the Lanczos algorithm [0.8181983928344693]
  We obtain an open two-mode squeezed state as the quantum origin for the curvature perturbation.<n>We calculate its corresponding power spectrum by using the Bogoliubov transformation.<n>Our research may offer a new insight into the calculation of the correlation functions through a group-theoretic perspective.
  arXiv  Detail & Related papers  (2025-05-27T00:10:41Z)
• Critical Dynamics of Spin Boson Model [0.0]
  We study the low-energy properties of the spin-boson model (SBM)<n>We study the critical dynamics of the system near the quantum phase transition.
  arXiv  Detail & Related papers  (2025-01-21T19:05:04Z)
• Emergent quantum Majorana metal from a chiral spin liquid [50.56734933757366]
  We propose a mechanism to explain the emergence of an intermediate gapless spin liquid phase in the antiferromagnetic Kitaev model.<n>We show that the Majorana spectral function captures the dynamical spin and dimer correlations obtained by the infinite Projectedangled Pair States method.
  arXiv  Detail & Related papers  (2024-05-20T18:00:01Z)
• 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)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Real-Space, Real-Time Approach to Quantum-Electrodynamical Time-Dependent Density Functional Theory [55.41644538483948]
  The equations are solved by time propagating the wave function on a tensor product of a Fock-space and real-space grid. Examples include the coupling strength and light frequency dependence of the energies, wave functions, optical absorption spectra, and Rabi splitting magnitudes in cavities.
  arXiv  Detail & Related papers  (2022-09-01T18:49:51Z)
• 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)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.