To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory. (arXiv:1906.02063v2 [hep-th] UPDATED)
We make comments on some shortcomings of the non-unitary-invariant and non-bi-invariant complexity in quantum mechanics/field theory and argue that the unitary-invariant and bi-invariant complexity is still a competitive candidate in quantum mechanics/field theory, contrary to quantum circuits in quantum computation. Based on the unitary-invariance of the complexity and intuitions from the holographic complexity, we propose a novel complexity formula between two states. Our proposal shows that i) the complexity between certain states in two dimensional CFTs is given by the Liouville action, which is compatible with the path-integral complexity; ii) it also gives natural interpretation for both the CV and CA holographic conjectures and identify what the reference states are in both cases. Our proposal explicitly produces the conjectured time dependence of the complexity: linear growth in chaotic systems. Last but not least, we present interesting relations between the complexity and the Lyapunov exponent: the Lyapunov exponent is proportional to the complexity growth rate in linear growth region.
Authors: G.W. Gibbons
Two lectures given in Paris in 1985. They were circulated as a preprint Solitons And Black Holes In Four-Dimensions, Five-Dimensions. G.W. Gibbons (Cambridge U.) . PRINT-85-0958 (CAMBRIDGE), (Received Dec 1985). 14pp. and appeared in print in De Vega, H.J. ( Ed.), Sanchez, N. ( Ed.) : Field Theory, Quantum Gravity and Strings*, 46-59 and Preprint – GIBBONS, G.W. (REC.OCT.85) 14p.
I have scanned the original, reformatted and and corrected various typos.
Modified Special Relativity (HMSR) — A new possible way to introduce an isotropic Lorentz Invariance Violation in particle Standard Model. (arXiv:1906.05595v1 [hep-th])
This work explores a Standard Model (S.M.) extension possibility, that violates Lorentz invariance, preserving the space-time isotropy and homogeneity. In this sense HMSR represents an attempt to introduce an isotropic Lorentz Invariance Violation in the elementary particle S.M. The theory is constructed starting from a modified kinematics, that takes into account supposed quantum effects due to interaction with the space-time background. The space-time structure itself is modified, resulting in a pseudo-Finsler manifold. The S.M. extension here provided is inspired by the effective fields theories, but it preserves covariance, with respect to newly introduced modified Lorentz transformations. Geometry perturbations are not considered as universal, but particle species dependent. Non universal character of the amended Lorentz transformations allows to obtain visible physical effects, detectable in experiments by comparing different perturbations related to different interacting particles species.
Authors: Louis Marchildon
All investigators working on the foundations of quantum mechanics agree that the theory has profoundly modified our conception of reality. But there ends the consensus. The unproblematic formalism of the theory gives rise to a number of very different interpretations, each of which has consequences on the notion of reality. This paper analyses how the Copenhagen interpretation, von Neumann’s state vector collapse, Bohm and de Broglie’s pilot wave and Everett’s many worlds modify, each in its own way, the classical conception of reality, whose local character, in particular, requires revision.
Can the quantum vacuum fluctuations really solve the cosmological constant problem?. (arXiv:1906.05406v1 [gr-qc])
Recently it has been argued that a correct reading of the quantum fluctuations of the vacuum could lead to a solution to the cosmological constant problem. In this work we critically examine such a proposal, finding it questionable due to conceptual and self-consistency problems, as well as issues with the actual calculations. We conclude that the proposal is inadequate as a solution to the cosmological constant problem.
Recent group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all the experiments. Among these assumptions is fair sampling, no signaling and faithful quantum model. We examined the data from 9 of 13 experiments and analyzed occurring anomalies in view of the above assumption. We conclude that further tests of local realism need better setup calibration to avoid apparent signaling or necessity of the complicated underlying quantum model.
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This, in turn, has recently led to applications to the study of entanglement in systems of identical particles. In the course of those investigations on entanglement and particle identity, an emergent gauge symmetry has been found by Balachandran, de Queiroz and Vaidya. In this letter we establish a novel connection between that gauge symmetry, entropy production and quantum operations. Thus, let A be a system described by a finite dimensional observable algebra and $\omega$ a mixed faithful state. Using the Gelfand-Naimark-Segal (GNS) representation we construct a canonical purification of $\omega$, allowing us to embed A into a larger system C. Using Tomita-Takasaki theory, we obtain a subsystem decomposition of C into subsystems A and B, without making use of any tensor product structure. We identify a group of transformations that acts as a gauge group on A while at the same time giving rise to entropy increasing quantum operations on C. We provide physical means to simulate this gauge symmetry/quantum operation duality.