Related papers: Nonrelativistic Lee model in three dimensional Rie…
This work is a continuation of our previous work (JMP, Vol. 48, 12, pp. 122103-1-122103-20, 2007), where we constructed the non-relativistic Lee model in three dimensional Riemannian manifolds. Here we renormalize the two dimensional…
We study the relativistic Lee model on static Riemannian manifolds. The model is constructed nonperturbatively through its resolvent, which is based on the so-called principal operator and the heat kernel techniques. It is shown that making…
In the present work, we first briefly sketch construction of the nonrelativistic Lee model on Riemannian manifolds, introduced in our previous works. In this approach, the renormalized resolvent of the system is expressed in terms of a…
We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem…
We show that the $L^p$ boundedness, $p>2$, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize…
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…
We reexamine the relativistic 2+1 dimensional Lee model in light-front coordinates on flat space and on a space-time with a spatial section given by a compact manifold in the usual canonical formalism. The simpler 2+1 dimension is chosen…
We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral…
We consider a class of manifolds $\mathcal{M}$ obtained by taking the connected sum of a finite number of $N$-dimensional Riemannian manifolds of the form $(\mathbb{R}^{n_i}, \delta) \times (\mathcal{M}_i, g)$, where $\mathcal{M}_i$ is a…
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…
We study the interaction of mutually non-interacting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant…
This paper addresses the computation of ground states of multicomponent Bose-Einstein condensates, defined as the global minimiser of an energy functional on an infinite-dimensional generalised oblique manifold. We establish the existence…
The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The…
A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat…
We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can…
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been…
We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the…
The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult,…
We study the low-energy approximation for calculation of the heat kernel which is determined by the strong slowly varying background fields in strongly curved quasi-homogeneous manifolds. A new covariant algebraic approach, based on taking…
We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports…