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Abelian Gauge Theories are quantized in a geometric representation that generalizes the Loop Representation and treates electric and magnetic operators on the same footing. The usual canonical algebra is turned into a topological algebra of…
A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes the analogous…
As large-scale multimode Gaussian states begin to become accessible in the laboratory, their representation and analysis become a useful topic of research in their own right. The graphical calculus for Gaussian pure states provides powerful…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
Associated to quantum affine general linear Lie superalgebras are two families of short exact sequences of representations whose first and third terms are irreducible: the Baxter TQ relations involving infinite-dimensional representations;…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and…
We present macrofacet theory to extend microfacet theory from the micro-space to the macro-space. This is achieved by transforming surfaces into volumetric representations that preserve microfacet characteristics. Therefore, we formulate a…
We generalise the Gaussian formalism of Continuous Variable (CV) systems to describe their interactions with qubits/qudits that result in quantum superpositions of Gaussian processes. To this end, we derive a new set of equations in closed…
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of…
Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymptotic expressions for the points and weights of Gaussian…
We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by an abstract $*-$algebra generated by a countable set of elementary operators labelled…
We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
A Hamiltonian lattice formulation of lattice gauge theories opens the possibility for quantum simulations of the non-perturbative dynamics of QCD. By parametrizing the gauge invariant Hilbert space in terms of plaquette degrees of freedom,…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and the s.c. "gravitational theories with covariant and contravariant connection and metrics", it is…