相关论文: Information geometry and Frobenius algebra

We construct a model of the Cyclic Universe from a joint theory of General relativity, Thermodynamics and Quantum information theory. Friedmann equations and the thermodynamical Gibbs-Duhem relation determine a general form of the Hubble…

The Yukawa interaction is considered in 0+1 dimensions as a pedagogical example to illustrate quantum field theory methods. From the quantum mechanical point of view the system is trivially exactly solvable, but this can be difficult to see…

In information geometry, one of the basic problem is to study the geomet-ric properties of statistical manifold. In this paper, we study the geometricstructure of the generalized normal distribution manifold and show that it has constant…

We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…

In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…

Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking…

An information measure inspired by Onicescu's information energy and Uffink's information measure (recently discussed by Brukner and Zeilinger) are calculated as functions of the number of particles $N$ for fermionic systems (nuclei and…

The Standard Model of particle physics is standardly formulated in terms of principal fibre bundles and their associated representations -- what may be called a symmetry-first approach. This paper develops an alternative geometry-first…

For many years, theorists have calculated formulas for useful quantities in general gauge-Yukawa theories. However, these cookbooks are often very difficult to use since the general notation is far removed from practical model building. In…

The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…

The primary objects of study in information geometry are statistical manifolds, which are parametrized families of probability measures, induced with the Fisher-Rao metric and a pair of torsion-free conjugate connections. In recent work,…

This paper illustrates the resemblance between the information-geometric structures of probability spaces and that of the discrete spectrum for Hawking radiation. The information geometry gives rise to a reconstruction of the standard…

We study elementary classical and quantum dynamics in an information geometric space corresponding to a Bernoulli random variable, extending work by Goehle and Griffin [Chaos, Solitons & Fractals, 188, 115535, (2024)], who study the…

A Frobenius manifold is a manifold with a flat metric and a Frobenius algebra structure on tangent spaces at points of the manifold such that the structure constants of multiplication are given by third derivatives of a potential function…

In this paper, we explicitly prove that statistical manifolds, related to exponential families and with flat structure connection have a Frobenius manifold structure. This latter object, at the interplay of beautiful interactions between…

A non perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs-Yukawa theory on a unit…

The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…

This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…

In Calabi--Yau compactifications of the heterotic string there exist quantities which are universal in the sense that they are present in every Calabi--Yau string vacuum. It is shown that such universal characteristics provide numerical…

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…