Related papers: Relativistic Lee Model on Riemannian Manifolds
In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace-Beltrami operator on M. We assume that the kernel associated to…
The absence of fermionic, asymptotical one-particle states in the Luttinger model raises the suspicion that the interactions are actually strong at the vicinity of the Fermi points. The functional internal space renormalization group…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
The asymptotic behavior of the effective mass $m_{\rm eff}(\Lambda)$ of the so-called Nelson model in quantum field theory is considered, where $\Lambda$ is an ultraviolet cutoff parameter of the model. Let $m$ be the bare mass of the…
Let $M$ be an $n(>2)$-dimensional closed orientable submanifold in an $(n+p)$-dimensional space form $\mathbb{R}^{n+p}(c)$. We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on $M$ defined by…
The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that,…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
Every linear system of partial differential equations (PDEs) admits a scaling symmetry in its dependent variables. In conjunction with other admitted symmetries of linear type, the associated invariant solution condition poses a linear…
Models of relativistic particle with Lagrangian ${\cal L}(k_1)$, depending on the curvature of the worldline $k_1$, are considered. By making use of the Frenet basis, the equations of motion are reformulated in terms of the principal…
We construct supersymmetric conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use the Wilsonian renormalization group equation method, which is one of the…
We consider diatomic systems in which the kinetic energy of the electrons is treated in a simple relativistic model. The Born-Oppenheimer approximation is assumed. We investigate questions of stability, deducing bounds on the number $N$ of…
We consider a four-dimensional theory in the z=3 Lifshitz context, with an exponential (Liouville) potential. We determine the exact renormalized potential of the theory and derive the non-perturbative relation between the renormalized and…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of…
Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d +…
Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is…
We study two-dimensional ferromagnetic Ising model on a series of regular lattices, which are represented as the tessellation of polygons with p>=5 sides, such as pentagons (p=5), hexagons (p=6), etc. Such lattices are on hyperbolic planes,…
Diffusion limits provide a framework for the asymptotic analysis of stochastic gradient descent (SGD) schemes used in machine learning. We consider an alternative framework, the Riemannian Langevin equation (RLE), that generalizes the…