Related papers: Causality and Localization Operators
Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance…
The paper deals with spectral analysis of non-local operators arising in population dynamics models. We consider negative periodic perturbations of non-local operators of the convolution type. Such operators describe evolutions of the first…
Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some…
The causality properties of linear time-varing systems under constant time lags are investigated based on the definition and use of the definitions of appropriate Hankel and Toeplitz causal and anticausal operators.
We show that fluctuations of bulk operators that are restricted to some region of space scale as the surface area of the region, independently of its geometry. Specifically, we consider two point functions of operators that are integrals…
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic…
A generalization of the operator product expansion for Euclidean correlators of gauge invariant QCD currents is presented. Each contribution to the modified expansion, which is based on a delocalized multipole expansion of a perturbatively…
In this paper a nonlocal generalization of field quantization is suggested. This quantization principle presupposes the assumption that the commutator between a field operator an the operator of the canonical conjugated variable referring…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be…
A scalar valued random field is called operator-scaling if it satisfies a self-similarity property for some matrix E with positive real parts of the eigenvalues. We present a moving average and a harmonizable representation of stable…
Requiring both that a proposed localization-density operator be linear in quantum theory and that its expectation value be covariant leads to addition of terms in the Hamiltonian, coupling a scalar field to a connection on the…
Using symmetric boundary conditions at separated times, I show analytically that both the time ordering of (macroscopic) causality and the direction of entropy increase follow from these boundary conditions. In particular, when the…
In this paper, we explore the questions of time, locality and causality in the framework of covariant open bosonic string field theory. We show that if an open string field is expressed as a certain local function on spacetime--in…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
We prove the existence of a weak solution for boundary value problems driven by a mixed local--nonlocal operator. The main novelty is that such an operator is allowed to be nonpositive definite.
Multivariate random fields whose distributions are invariant under operator-scalings in both time-domain and state space are studied. Such random fields are called operator-self-similar random fields and their scaling operators are…
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two…