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The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional…
In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both…
Higher order coefficients of the inverse mass expansion of one--loop effective actions are obtained from a one--dimensional path integral representation. For the evaluation of the path integral with Wick contractions a suitable Green…
Our aging population increasingly suffers from multiple chronic diseases simultaneously, necessitating the comprehensive treatment of these conditions. Finding the optimal set of drugs for a combinatorial set of diseases is a combinatorial…
We introduce a new isomorphism-invariant notion of entropy for measure preserving actions of arbitrary countable groups on probability spaces, which we call orbital Rokhlin entropy. It employs Danilenko's orbital approach to entropy of a…
In this note we do the analysis of entanglement entropy more carefully when the non-conformal theory flows to a non-trivial IR fixed point. In particular we emphasize the role of the trace of the energy-momentum tensor in these…
Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using…
For the case of reduction onto the non-zero momentum level, in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimle…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
Spin sum rules depend on the choice of a pivot, i.e. the point about which the angular momentun is defined, usually identified with the center of the nucleon. The latter is however not unique in a relativistic theory and has led to…
Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field,…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Based on a reconsideration of the Gibbs paradox, we show that a residual, non-extensive term in entropy turns up upon mixing identical particles, whether they are indistinguishable or not. The positive contribution from this residual…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
We review a formulation of the entanglement entropy of a quantum scalar field in terms of its spacetime two-point correlation functions. We discuss applications of this formulation to studying entanglement entropy in various settings in…
The conjectures of Low and Natario--Tod, and Penrose's question on Arnold's Problem list ask if causality in spacetimes can be formulated in terms of linking of spheres of light rays in the manifold of all light rays. For…
A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its transpose allows us to show that for a more complicated network,…
For higher derivative theories of gravity, it is possible to write the action in terms of auxiliary fields. In such case, one can show that the equations of motion for both actions are equivalent and hence the actions themselves. In this…
I present aspects of causal set theory (a research programme in quantum gravity) as being en route to achieving a reduction of Lorentzian geometry to causal sets. I take reduction in philosophers' sense; and I argue that the prospects are…
Bell's theorem shows that our intuitive understanding of causation must be overturned in light of quantum correlations. Nevertheless, quantum mechanics does not permit signalling and hence a notion of cause remains. Understanding this…