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We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical…
In this paper we study the su(m) spin Sutherland (trigonometric) model of D_N type and its related spin chain of Haldane-Shastry type obtained by means of Polychronakos's freezing trick. As in the rational case recently studied by the…
We review recent progress in formulating two-dimensional models over noncommutative manifolds where the space-time coordinates enter in the formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to approximate…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
We study the fully itinerant dynamics of ultracold but nondegenerate polar molecules with a spin-$1/2$ degree of freedom encoded into two of their electric field dressed rotational states. Center of mass molecular motion is constrained to…
The 1-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them Loop Quantum Gravity and Spin Foams. It facilitates the loop quantization…
The Sample Compression Conjecture of Littlestone & Warmuth has remained unsolved for over two decades. This paper presents a systematic geometric investigation of the compression of finite maximum concept classes. Simple arrangements of…
We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ…
We investigate the effect of periodic driving by an external field on systems with attractive pairing interactions. These include spin systems (like the ferromagnetic XXZ model) as well as ultracold fermionic atoms described by the…
Spin foams arise from a quantization of classical gravity expressed via the Plebanski action. Key open questions related to the continuum limit of spin foams are whether general relativity is reproduced and what type of corrections could…
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well…
We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two…
Reduced-order models (ROMs) have become an essential tool for reducing the computational cost of fluid flow simulations. While standard ROMs can efficiently approximate laminar flows, their accuracy often suffers in convection-dominated…
The five-band Hubbard model for a $d$ band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e. g. cubic) symmetry. In that case, if the crystal field…
I discuss the use of spinors in the construction of spin-foam models, in particular the form of the closure and simplicity constraints for triangles that are space-like, i.e. with (area)$^2=\half S^{IJ}S_{IJ}>0$, regardless of whether they…
Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…
Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we show the existence of (i) a couple of off-shell nilpotent (i.e. fermionic) BRST and co-BRST symmetry transformations, and (ii) a full set of non-nilpotent (i.e. bosonic)…
Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic…
The necessary and sufficient conditions to construct consistent Lagrangian formulation for irreducible interacting massless higher-spin (HS) fields on $d$-dimensional Minkowski space within approach with incomplete BRST operator and…