Related papers: Reflection Positivity for Parafermions
We propose a scheme combining spin reflection positivity and generalized hole-particle and orbital transformations to characterize the symmetry properties of the ground state for some correlated electron models on bipartite lattices. In…
We show how a strongly coupled lattice theory consisting of just fermions and gauge fields can exhibit a dynamical Higgs mechanism through the formation of a gauge invariant four fermion condensate. Furthermore, we argue that this lattice…
I review recent progress in the implementation of lattice fermions satisfying the Ginsparg-Wilson relation and some physical applications.
In this work we investigate $q{\bar q}$ spectra and wavefunctions of light front transverse lattice Hamiltonians that result from different methods of formulating fermions on the transverse lattice. We adopt the one link approximation for…
We review the complex differential geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ and give a description of Hamilton's characteristic functions for reflection in an oriented C$^1$ surface in terms of this geometry.
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a…
Epitaxy of semiconductors is a process of tremendous importance in applied science and optoelectronic industry. Controlling of defects introduced during epitaxial growth is a key point in manufacturing devices of high efficiency and…
We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a…
We study the gauge fixing of lattice QCD in 2+1 dimensions, in the Hamiltonian formulation. The technique easily generalizes to other theories and dimensions. The Hamiltonian is rewritten in terms of variables which are gauge invariant…
In our earlier work arXiv:2311.09334, we introduced a lattice Hamiltonian for Adjoint QCD$_2$ using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group $\text{SU}(2)$ and used them for…
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons"…
A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.
Comparing random lattice, naive and Wilson fermions in two dimensional abelian background gauge field, we show that the doublers suppressed in the free field case are revived for random lattices in the continuum limit unless gauge…
We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory and duality between unitary representations of the euclidean motion group and the Poincare group. On the…
The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.
We investigate consequences of the effective colour-dielectric formulation of lattice gauge theory using the light-cone Hamiltonian formalism with a transverse lattice (hep-ph/9704408). As a quantitative test of this approach, we have…
We consider the lateral shift of a light beam reflecting from a dielectric slab backed by a metal. It is found that the lateral shift of the reflected beam can be negative while the intensity of reflected beam is almost equal to the…