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Starting from a solution to the classical Batalin-Vilkovisky master equation,an extended solution to an extended master equation is constructed by coupling all the observables, the anomaly candidates and the generators of global symmetries.…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
This paper contributes to the solution of the problem of transforming a process model with an arbitrary topology into an equivalent structured process model. In particular, this paper addresses the subclass of process models that have no…
We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
Relation-changing modal logics are extensions of the basic modal logic that allow changes to the accessibility relation of a model during the evaluation of a formula. In particular, they are equipped with dynamic modalities that are able to…
We present an integral formalism for constructing scheme transformations in a quantum field theory. We apply this to generate several new useful scheme transformations. A comparative analysis is given of these scheme transformations in…
The electronic properties of nanoscale quantum dots are reviewed. The similarities and differences between these `artificial atoms' and real atoms are discussed and, in particular, the effect of electron correlations is examined. It is…
New superintegrable systems are presented which, like the Hydrogen atom, possess a dynamical symmetry w.r.t. algebra o(4). One of them simulates a neutral fermion with non-trivial dipole moment, interacting with the external e.m. field.…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments…
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager…
An analogue of the mixing property of quantum entropy is derived for quantum relative entropy.It is applied to the final state of ideal measurement and to the spectral form of the second density operator. Three cases of states on a directed…
This study utilizes theoretical tools including the double copy relation and AdS/CFT correspondence. Applying analogies, we establish a system to discuss the associations and equivalence relations among QCD, QED, and various (mixed) gauge…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
Previous papers give accounts of quests for satisfactory formalizations of the classical informal notion of an algorithm and the contemporary informal notion of an interactive algoritm. In this paper, an attempt is made to generalize the…
New results and improvements in the study of nonparametric exponential and mixture models are proposed. In particular, different equivalent characterizations of maximal exponential models, in terms of open exponential arcs and Orlicz…
In this paper we introduce the theory of multiplication alteration by two-cocycles for nonassociative structures like nonassociative bimonoids with left (right) division. Also we explore the connections between Yetter-Drinfeld modules for…
This PHD thesis hinges on the terms mentioned in the title. It introduces a formalism which allows one to find equalities generalizing the formula of Mark Kac which deals with a measure-preserving transformation. The formalism is meaningful…