scholarly journals Density matrices in quantum gravity

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Tarek Anous ◽  
Jorrit Kruthoff ◽  
Raghu Mahajan
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Free Choice ◽  
Global State ◽  
Density Matrices ◽  
Topology Change ◽  
One Dimensional ◽  
Strong Subadditivity ◽  
The Third ◽  
Klein Gordon

We study density matrices in quantum gravity, focusing on topology change. We argue that the inclusion of bra-ket wormholes in the gravity path integral is not a free choice, but is dictated by the specification of a global state in the multi-universe Hilbert space. Specifically, the Hartle-Hawking (HH) state does not contain bra-ket wormholes. It has recently been pointed out that bra-ket wormholes are needed to avoid potential bags-of-gold and strong subadditivity paradoxes, suggesting a problem with the HH state. Nevertheless, in regimes with a single large connected universe, approximate bra-ket wormholes can emerge by tracing over the unobserved universes. More drastic possibilities are that the HH state is non-perturbatively gauge equivalent to a state with bra-ket wormholes, or that the third-quantized Hilbert space is one-dimensional. Along the way we draw some helpful lessons from the well-known relation between worldline gravity and Klein-Gordon theory. In particular, the commutativity of boundary-creating operators, which is necessary for constructing the alpha states and having a dual ensemble interpretation, is subtle. For instance, in the worldline gravity example, the Klein-Gordon field operators do not commute at timelike separation.

scholarly journals Clock-dependent spacetime

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sung-Sik Lee
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Gravity ◽  
Hilbert Spaces ◽  
Coordinate Systems ◽  
Physical Laws

Abstract Einstein’s theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

scholarly journals Gap breathers in the one-dimensional Klein-Gordon diatomic chain

2007 ◽  
Vol 56 (2) ◽  
pp. 1041
Author(s):  
Li Mi-Shan ◽  
Tian Qiang
Keyword(s):  
One Dimensional ◽  
Diatomic Chain ◽  
Klein Gordon ◽  
The One

scholarly journals The Rethinking of Great Britain’s Role: From the World Empire to the Nation State

2019 ◽  
pp. 129-145
Author(s):  
O. Zernetska
Keyword(s):  
Great Britain ◽  
British Empire ◽  
Nation State ◽  
Global State ◽  
The Third ◽  
The World ◽  
Commonwealth Of Nations ◽  
British Commonwealth ◽  
British Commonwealth Of Nations ◽  
Different Parts

In the article, it is stated that Great Britain had been the biggest empire in the world in the course of many centuries. Due to synchronic and diachronic approaches it was detected time simultaneousness of the British Empire’s development in the different parts of the world. Different forms of its ruling (colonies, dominions, other territories under her auspice) manifested this phenomenon.The British Empire went through evolution from the First British Empire which was developed on the count mostly of the trade of slaves and slavery as a whole to the Second British Empire when itcolonized one of the biggest states of the world India and some other countries of the East; to the Third British Empire where it colonized countries practically on all the continents of the world. TheForth British Empire signifies the stage of its decomposition and almost total down fall in the second half of the 20th century. It is shown how the national liberation moments starting in India and endingin Africa undermined the British Empire’s power, which couldn’t control the territories, no more. The foundation of the independent nation state of Great Britain free of colonies did not lead to lossof the imperial spirit of its establishment, which is manifested in its practical deeds – Organization of the British Commonwealth of Nations, which later on was called the Commonwealth, Brexit and so on.The conclusions are drawn that Great Britain makes certain efforts to become a global state again.

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