Related papers: Nonlinear $\sigma$-Model in (2+1) dimensions
The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor {\theta} present; no…
We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By…
We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to…
We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the…
The coexistence of superconducting and charge-density-wave order in the half-filled attractive Hubbard model is interpreted as a consequence of the pseudospin SU(2) symmetry spontaneously broken to a `hidden' subgroup U(1). By topological…
Non-linear effects and non-Hermitian phenomena unveil additional intricate facets in topological matter physics. They can naturally intertwine to enable advanced functionalities in topoelectrical circuits and photonic structures. Here, we…
The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The…
We present a new $(2+1)$-dimensional field theory showing exotic statistics and fractional spin. This theory is achieved through a redefinition of the gauge field $A_{\mu}$. New properties are found. Another way to implement the field…
Nonlinear Dirac equations in D+1 space-time are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1…
In this work, a possible description for quantum dynamics of the cuscuton within the sigma-model approach is presented. Lower order perturbative corrections and the structure of divergences are found. Motivated by the results generated by…
We consider 2+1 dimensional noncommutative models of scalar and fermionic fields coupled to the Chern-Simons field. We show that, at least up to one loop, the model containing only a fermionic field in the fundamental representation…
The spin 1 bilinear-biquadratic model on square lattice in the region $0<\phi<\pi/4$ is studied in a fermion representation with a p-wave pairing BCS type mean-field theory. Our results show there may exist a non-trivial gapped spin liquid…
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$…
Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be…
In terms of non-commutative geometry, we show that the $\sigma$--model can be built up by the gauge theory on discrete group $Z_2$. We introduce a constraint in the gauge theory, which lead to the constraint imposed on linear $\sigma$ model…
We construct the non-standard Lagrangian, called the multiplicative form, of the homogeneous scalar field and fermion field through the inverse calculus of variations, which the equation of motion still satisfies the Klein-Gordon and Dirac…
The fermion representation for S = 1/2 spins is generalized to spins with arbitrary magnitudes. The symmetry properties of the representation is analyzed where we find that the particle-hole symmetry in the spinon Hilbert space of S =1/2…
We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z_2-graded Poisson, or quantum super- algebra, which may be treated as a…