Quantum singularities in Hořava-Lifshitz cosmology

João Paulo M. Pitelli; Alberto Saa

doi:10.1103/physrevd.86.063506

Quantum Singularities in Macroscopic Measurements

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.0122.197705g.0164 ◽

1977 ◽

Vol 122 (5) ◽

pp. 164 ◽

Cited By ~ 1

Author(s):

Vladimir B. Braginskii

Keyword(s):

Quantum Singularities

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QUANTUM SINGULARITIES IN STATIC SPACETIMES

International Journal of Modern Physics D ◽

10.1142/s0218271811019062 ◽

2011 ◽

Vol 20 (05) ◽

pp. 729-743 ◽

Cited By ~ 17

Author(s):

JOÃO PAULO M. PITELLI ◽

PATRICIO S. LETELIER

Keyword(s):

Quantum Mechanics ◽

Wave Operator ◽

Point Of View ◽

Quantum Mechanical ◽

Mathematical Framework ◽

Physical Content ◽

Dirac Equations ◽

Quantum Particles ◽

Klein Gordon ◽

Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

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Quantum Singularities in Conformally Static Spacetimes

Springer Proceedings in Physics - Relativity and Gravitation ◽

10.1007/978-3-319-06761-2_75 ◽

2014 ◽

pp. 539-545

Author(s):

Deborah A. Konkowski ◽

Thomas M. Helliwell

Keyword(s):

Quantum Singularities

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PHYSICS OF SINGULAR POINTS IN QUANTUM MECHANICS

International Journal of Quantum Information ◽

10.1142/s0219749903000413 ◽

2003 ◽

Vol 01 (04) ◽

pp. 543-560 ◽

Cited By ~ 3

Author(s):

IZUMI TSUTSUI ◽

TAMÁS FÜLÖP

Keyword(s):

Quantum Mechanics ◽

Berry Phase ◽

Singular Points ◽

One Dimension ◽

Partition Wall ◽

Quantum Singularities ◽

Quantum Force ◽

Physical Phenomena ◽

Particle Statistics ◽

Behavior Characteristic

Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an unexpectedly rich structure and thereby provide a variety of physical phenomena, especially if their properties are controlled properly. Based on our recent studies, we present a brief review on the physical aspects of such quantum singularities in one dimension. Among the intriguing phenomena that the singularities admit, we mention strong versus weak duality, supersymmetry, quantum anholonomy (Berry phase), and a copying process by anomalous caustics. We also show that a partition wall as a singularity in a potential well can give rise to a quantum force which exhibits an interesting temperature behavior characteristic to the particle statistics.

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QUANTUM SINGULARITIES IN STATIC AND CONFORMALLY STATIC SPACE-TIMES

International Journal of Modern Physics A ◽

10.1142/s0217751x11054334 ◽

2011 ◽

Vol 26 (22) ◽

pp. 3878-3888 ◽

Cited By ~ 12

Author(s):

D. A. KONKOWSKI ◽

T. M. HELLIWELL

Keyword(s):

Power Law ◽

Cosmic String ◽

Higher Order ◽

Space Time ◽

Differential Invariants ◽

Future Research ◽

Quantum Singularities ◽

Definition Of ◽

Friedmann Robertson Walker ◽

Static Space

The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by an example, a Friedmann-Robertson-Walker space-time with cosmic string. The paper concludes by discussing areas of future research.

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