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A discussion of the number of degrees of freedom, and their dynamical properties, in higher-derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
We analyze newly expanded and refined data from lattice studies of an SU(3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of…
Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and…
We study the contribution of the torsion-descendent four-fermion contact interaction to the decay width of a neutral (pseudo)scalar field into a fermion pair. This new interaction comes from the existence of gravitational torsion in models…
The model of dense lattice polymers is studied as an example of non-unitary Conformal Field Theory (CFT) with $c=-2$. ``Antisymmetric'' correlation functions of the model are proved to be given by the generalized Kirchhoff theorem.…
We have studied free higher spin gauge fields through an investigation of their Hamiltonian dynamics. Over a flat space-time, their Hamiltonian constraints were identified and solved through the introduction of prepotentials, enjoying both…
We study the phase diagram of interacting spinless fermions on the honeycomb bilayer at charge neutrality using large-scale quantum Monte Carlo simulations. In the noninteracting limit, the low-energy spectrum features quadratically…
Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an…
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories…
A method used recently to obtain a formalism for classical fields with non-local actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens' principle with free discrete propagators that recover…
Quadratic band touching in fermionic systems defines a universality class distinct from that of linear Dirac points, yet its characterization as a quantum critical point remains incomplete. In this work, I show that a $(d+1)$-dimensional…
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…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
This is a discussion on degrees of freedom of massless fermion and boson fields, if they are free or weakly interacting. We generalize the gauge fields of $S^{ab}$ - $\omega_{abc}$ - and of $\tilde{S}^{ab}$ - $ \tilde{\omega}_{abc}$ - of…
We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh…
In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but…
A new method of abstracting the independent gauge invariances of higher derivative systems, recently introduced in [1], has been applied to higher derivative field theories. This has been discussed taking the extended Maxwell-Chern-Simons…
In this thesis, we perform a comprehensive renormalization group analysis of two- and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by…
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $\pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total…
In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and…