Related papers: Grassmann techniques applied to classical spin sys…
Functional integral methods provide a way to define mean--field theories and to systematically improve them. For the Hubbard model and similar strong--correlation problems, methods based in particular on the Hubbard--Stratonovich…
The actions for all classical (and consequently quantum) $BF$ theories on $n$-manifolds is proven to be given by anti-commutators of hermitian, nilpotent, scalar fermionic charges with Grassmann-odd functionals. In order to show this, the…
Duality transformations play a very important role in theoretical physics. In this paper I propose new duality transformations for fermionic theories. They map the strong coupling regime of one theory to the weak coupling regime of another…
In a space of $d $ Grassmann coordinates two types of generators of Lorentz transformations can be defined, one of spinorial and the other of vectorial character. Both kinds of operators appear as linear operators in Grassmann space,…
The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…
In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution…
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…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the…
We build the asymptotic higher-spin charges associated with "improper" gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We…
We apply a new updating algorithm scheme to investigate the critical behavior of the two-dimensional ferromagnetic Ising model on a triangular lattice with nearest neighbour interactions. The transition is examined by generating accurate…
We study spontaneous symmetry breaking in quantum field theories with fermionic order parameters and construct, for the first time in the literature, the constraint effective potential for it. The Grassmann-valued constraint we encounter is…
We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a…
We discuss the formulation of spin observables associated to a non-relativistic spinning particles in terms of grassmanian differential operators. We use as configuration space variables for the pseudo-classical description of this system…
On the basis of the qualitative analysis and numerical simulation of cosmological models with classical and phantom scalar fields with self-action there have been revealed and refined such models' distinctive features and potential…
We present the result of the spin-orbit interaction Hamiltonian for binary systems of rotating compact objects with generic spins, up to NNNLO corrections within the post-Newtonian expansion. The calculation is performed by employing the…
We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of…
In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…
We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free field. Our theorem explains the microscopic origin of the sine-Gordon field theory…
We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac…