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The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2)…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed…
We review our efforts in investigating gauge theories with fermions in the adjoint representation of the gauge group by means of numerical simulations. These theories have applications in possible extensions of the Standard Model of…
Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to $U(1)$ quantum link gauge fields has…
We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be solved exactly via a simple unitary…
Fermion mass generation in the strongly coupled U(1) lattice gauge theory with fermion and scalar fields of equal charge is investigated by means of numerical simulation with dynamical fermions. Chiral symmetry of this model is broken by…
We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and…
The chiral fermion model with local multifermion interactions proposed in Nucl. Phys. B486 (1997) 282 and Phys. Rev. D61 (2000) 054502 processes an exact SU_L(2) chiral gauge symmetry and SU_L(2) by U_R(1) chiral flavour symmetry on a…
The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used…
We explore systematically the ground state properties of one dimensional fermions with long-range interactions decaying in a power law $\sim1/r^\alpha$ through the density matrix renormalization group algorithm. By comparing values of…
We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum…
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through…
Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in $d$ spatial dimensions with power-law decaying interactions…
Four fermion interactions appear in many models of Beyond Standard Model physics. In Technicolour and composite Higgs models Standard Model fermion masses can be generated by four fermion terms. They are also expected to modify the dynamics…
We study relativistic anyon field theory in 1+1 dimensions. While (2+1)-dimensional anyon fields are equivalent to boson or fermion fields coupled with the Chern-Simons gauge fields, (1+1)-dimensional anyon fields are equivalent to boson or…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
For a (2+1)-dimensional Born-Infeld theory coupled to a recently proposed generalized connection, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is…
Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the…
We prove a generalization of the Verlinde formula to fermionic rational conformal field theories. The fusion coefficients of the fermionic theory are equal to sums of fusion coefficients of its bosonic projection. In particular, fusion…