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We investigate the entropy bound for local quantum field theory in this paper. Both the bosonic and fermionic fields confined to an asymptotically flat spacetime are examined. By imposing the non-gravitational collapse condition, we find both of them are limited by the same entropy bound $A^{3/4}$, where $A$ is the boundary area of the region where the quantum fields are contained in. The gap between this entropy bound and the holographic entropy has been verified.
It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observers ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.
The problem of causality is analyzed in the context of Local Quantum Field Theory. Contrary to recent claims, it is shown that apparent noncausal behaviour is due to a lack of the notion of sharp localizability for a relativistic quantum system. (Replaced corrupted file)
A classical upper bound for quantum entropy is identified and illustrated, $0leq S_q leq ln (e sigma^2 / 2hbar)$, involving the variance $sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.
Recently, Cardy, Castro Alvaredo and the author obtained the first exponential correction to saturation of the bi-partite entanglement entropy at large region length, in massive two-dimensional integrable quantum field theory. It only depends on the particle content of the model, and not on the way particles scatter. Based on general analyticity arguments for form factors, we propose that this result is universal, and holds for any massive two-dimensional model (also out of integrability). We suggest a link of this result with counting pair creations far in the past.
We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain the results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy.