Non-Hermitian Hamiltonians in Quantum Physics pp 383-399 | Cite as

# Quantization of Big Bang in Crypto-Hermitian Heisenberg Picture

## Abstract

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 exceptional-point times \(t=\tau _{(EP)}\) 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 \(Q(\tau _{(EP)})\) acquire a non-diagonalizable Jordan-block structure. (3) During our “Eon” (i.e., at all \(t>\tau _{(EP)}\)) the observability status of operators *Q*(*t*) is guaranteed by their self-adjoint nature with respect to an *ad hoc* Hilbert-space metric \(\varTheta (t) \ne I\). (4) In adiabatic approximation the passage of the Universe through its \(t=\tau _{(EP)}\) singularity is interpreted as a quantum phase transition between the preceding and the present Eon.

## Keywords

Hilbert Space Quantum Phase Transition Unitary Evolution Exceptional Point Heisenberg Picture## References

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