Turning big bang into big bounce: II. Quantum dynamics

Małkiewicz, Przemysław; Piechocki, Włodzimierz

doi:10.1088/0264-9381/27/22/225018

Cited by 32 publications

(63 citation statements)

References 45 publications

(80 reference statements)

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“…A decisive weakness of the whole argument has already been noticed by Ashtekar et al [35,38,39]. The essence of the problem may be seen in the incompatibility of the quantized version of the degeneracy of eigenvalues (6) with the self-adjoint nature of the underlying operator.…”

Section: (T)mentioning

confidence: 99%

Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points

Znojil¹

2016

Symmetry

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For a given operator D(t) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t critical of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato's name of an "exceptional point", t critical = t (EP) . In the majority of conventional applications the exceptional point (EP) values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t (EP) become real. These values are interpreted as "instants of a catastrophe", be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology.

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Section: (T)mentioning

confidence: 99%

Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points

Znojil¹

2016

Symmetry

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“…also its published version [16]) which was delivered by Wlodzimierz Piechocki from Warsaw. In his talk the speaker analyzed the quantum Friedmann-RobertsonWalker model in the setting of loop quantum gravity [17].…”

Section: The Problem Of Survival Of Singularities After Quantizationmentioning

confidence: 99%

Quantization of Big Bang in Crypto-Hermitian Heisenberg Picture

Znojil¹

2016

Springer Proceedings in Physics

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A background-independent quantization of Universe near its Big Bang singularity is considered. Several conceptual issues are addressed in Heisenberg picture. (1) The observable spatial-geometry non-covariant characteristics of an empty-space expanding Universe are sampled by (quantized) distances Q = Q(t) between space-attached observers. (2) In Q(t) one of the Kato's exceptionalpoint times t = τ (EP ) is postulated real-valued. At such an instant the widely accepted "Big Bounce" regularization of the Big Bang singularity gets replaced by the full-fledged quantum degeneracy. Operators Q(τ (EP ) ) acquire a non-diagonalizable Jordan-block structure. (3) During our "Eon" (i.e., at all t > τ (EP ) ) the observability status of operators Q(t) is guaranteed by their self-adjoint nature with respect to an ad hoc Hilbert-space metric Θ(t) = I. (4) In adiabatic approximation the passage of the Universe through its t = τ (EP ) singularity is interpreted as a quantum phase transition between the preceding and the present Eon.

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“…p-brane and the embedding spacetime, by making use of the loop quantum cosmology. We have already made some preliminary steps to examine this problem [21,22].…”

Section: Jhep08(2010)054mentioning

confidence: 99%

Dirac quantization of membrane winding uniformly in time dependent orbifold

Małkiewicz¹,

Piechocki²

2010

J. High Energ. Phys.

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We present quantum theory of a membrane propagating in the vicinity of a time dependent orbifold singularity. The dynamics of a membrane, with the parameters space topology of a torus, winding uniformly around compact dimension of the embedding spacetime is mathematically equivalent to the dynamics of a closed string in a flat FRW spacetime. The construction of the physical Hilbert space of a membrane makes use of the kernel space of self-adjoint constraint operators. It is a subspace of the representation space of the constraints algebra. There exist non-trivial quantum states of a membrane evolving across the singularity.

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Turning big bang into big bounce: II. Quantum dynamics

Cited by 32 publications

References 45 publications

Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points

Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points

Quantization of Big Bang in Crypto-Hermitian Heisenberg Picture

Dirac quantization of membrane winding uniformly in time dependent orbifold

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