Related papers: How to Introduce Time Operator
The techniques employed to solve the interaction of a detector and a quantum field typically require perturbation methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with…
We compare two different approaches to the treatment of the Wheeler-DeWitt equation and the introduction of time in quantum cosmology. One approach is based on the gauge-fixing procedure in theories with first-class constraints, while the…
A new localization scheme for Klein-Gordon particle states is introduced in the form of general space and time operators. The definition of these operators is achieved by establishing a second quantum field in the momentum space of the…
Let $\{T_1, \ldots, T_n\}$ be a set of $n$ commuting bounded linear operators on a Hilbert space $\mathcal{H}$. Then the $n$-tuple $(T_1, \ldots, T_n)$ turns $\mathcal{H}$ into a module over $\mathbb{C}[z_1, \ldots, z_n]$ in the following…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the…
In this work we present a theoretical model for differentiable programming. We construct an algebraic language that encapsulates formal semantics of differentiable programs by way of Operational Calculus. The algebraic nature of Operational…
We relate the convergence of time-changed processes driven by fractional equations to the convergence of corresponding Dirichlet forms. The fractional equations we dealt with are obtained by considering a general fractional operator in…
The transfer operator associated to a flow (continuous time dynamical system) is a one-parameter operator semigroup. We consider the operator-valued Laplace transform of this one-parameter semigroup. Estimates on the Laplace transform have…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
We introduce Quantum Time-Frequency Analysis, which expands the approach of Quantum Harmonic Analysis to include modulations of operators in addition to translations. This is done by a projective representation of double-phase space, and we…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
We introduce the concept of an {\em operator decision making technique} and apply it to a concrete political problem: should a given political party form a coalition or not? We focus on the situation of three political parties, and divide…