Related papers: Quantum j-invariant in positive characteristic I: …
We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.
In the quantitative theory of quantum coherence, the amount of coherence for given states can be meaningfully discussed only when referring to a preferred basis. One of the objections to this quantification is that the amount of coherence…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
Based on a quantum mechanical approach, we investigate moment- (or M-) indeterminate probability densities by way of the characteristic function and self-adjoint operators. The approach leads to new methods to construct classes of…
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
We derive an action for scalar quantum field theory with cubic interaction in the context of relative locality. Beginning with the generating functional for standard $\varphi^3$--theory and the corresponding Feynman rules we modify them to…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…
In the work it is shown that the principles "the objective local theory" and corollaries of the standard quantum mechanics are not in such antagonistic inconsistency as it is usually supposed. In the framework of algebraic approach, the…
We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity,…
The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are…
The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…
The term quantum neural computing indicates a unity in the functioning of the brain. It assumes that the neural structures perform classical processing and that the virtual particles associated with the dynamical states of the structures…
We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of…
The aim of the current paper is to clarify some aspects of the formalism used for describing the scalar-tensor gravity characterized by four arbitrary local functionals of the scalar field. We recall the objects that are invariant with…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
The multiparameter quantum Pfaffian of the $(p, \lambda)$-quantum group is introduced and studied together with the quantum determinant, and an identity relating the two invariants is given. Generalization to the multiparameter…
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined.…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…