Space-time is four-dimensional

The quantum state of the universe is described by Hartle and Hawking's ground state which is defined by a path integral over all compact metrics. The most probable classical evolution of the universe can be considered to come from some gravitational instanton by a quantum tunneling. These arguments have been generalized to the case of Kaluza-Klein models. It is found that in d= 11 simple supergravity, with a minisuperspace ansatz, all instantons must have a four dimensional sector. It suggests that this is the main reason why space-time is four-dimensional.This essay received the third award from the Gravity Research Foundation for the year 1985—Ed.     

Loss of incoherence and determination of coupling constants in quantum gravity

The wave function of an interacting ‘family’ of one large ‘parent’ and many Planck-sized ‘baby’ universes is computed in a semiclassical approximation using an adaptation of Hartle-Hawking initial conditions. A recently discovered gravitational instanton which exists for general relativity coupled to axions is employed. The outcome of a single experiment in the parent universe is in general described by a mixed state, even if the initial state is pure. However, a sequence of measurements rapidly collapses the wave function of the family of universes into one of an infinite number of ‘coherent’ states for which quantum incoherence is not observed in the parent universe. This provides a concrete illustration of an unexpected phenomena whose existence has been argued for on quite general grounds by Coleman: quantum incoherence due to information loss to baby universes is not experimentally observable. We further argue that all coupling constants governing dynamics in the parent universe depend on the parameters describing the particular coherent state into which the family wave function collapses. In particular, generically terms that violate any global symmetries will be induced in the effective action for the parent universe. These last results have much broader applicability that our specific model.     

Letter: Quantum Kaluza-Klein Cosmologies

In the No-boundary Universe with d = 11 supergravity, under the S _n × S _11–n Kaluza-Klein ansatz, the only seed instanton for the universe creation is a S ₇ × S ₄ space. It is proven that for the Freund-Rubin, Englert and Awada-Duff-Pope models the macroscopic universe in which we are living must be 4- instead of 7-dimensional without appealing to the anthropic principle.     

Constrained instanton and black hole creation

It is generally accepted that the Einstein theory of general relativity governs the evolution of the universe. However, the singularity theorem of Hawking and Penrose[1] shows that under the most reasonable physical conditions, a spacetime singularity, where physics laws and even causality are broken down, is unavoidable. One has to impose the boundary or initial conditions at the edge of spacetime for the evolution of the universe. This is the so-called first cause problem. The no-boundary …     

Creation of Closed or Open Universe from Constrained Instanton

In the no-boundary universe the universe is created from an instanton. However, no instanton exists for the realistic FRW universe with a scalar field. The instanton leading to its quantum creation may be modified and reinterpreted as a constrained gravitational instanton.     

A new AF gravitational instanton

It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this Letter, we show that this conjecture is false by explicitly constructing a new two-parameter AF gravitational instanton with a U(1)×U(1) isometry group, using the inverse-scattering method. It has Euler number χ=3 and Hirzebruch signature τ=1, and its global topology is CP² with a circle S¹ removed appropriately. Various other properties of this gravitational instanton are also discussed.     

Dimensionality and the cosmological constant

In the Kaluza-Klein model with a cosmological constant Λ and a flux, the external spacetime of the created universe from aS ^s × S ^n−s seed instanton can be identified in quantum cosmology. One can also show that in the internal space theeffective cosmological constant is most probably zero.     

Berry phase in the gravitational quantum well and the Seiberg-Witten map

We explicitly compute the geometrical Berry phase for the noncommutative gravitational quantum well for different SW maps. We find that they lead to different partial contributions to the Berry phase. For the most general map we obtain that Δγ(S)∼η³, in a segment S of the path in the configuration space where is the fundamental momentum scale for the noncommutative gravitational quantum well. For the full closed path, we find, through an explicit computation, that γ(C)=0. This result is consistent with the fact that physical properties are independent of the SW map and shows that these maps do not introduce degeneracies or level crossing in the noncommutative extensions of the gravitational quantum well.     

Quantum Black Hole

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early universe, in the quantum cosmology scenario the black hole is essentially created from nothing. The black hole originates from a constrained gravitational instanton. The probability of creation for all kinds of single black holes in the Kerr-Newman family, at the semiclassical level, is the exponential of the total entropy of the universe, or one quarter of the sum of both the black hole and the cosmological horizon areas. The de Sitter spacetime is the most probable evolution at the Planckian era.     

Subsidiary conditions and physical S-matrix unitarity in indefinite-metric quantum gravitation theory

The quantum theory of gravitational fields is formulated in a manifestly Lorentz covariant manner in the framework of indefinite-metric quantum field theory. The physical state subspace is defined by the two subsidiary conditions Q_B|phys〉 = Q_c|phys〉 = 0, where the conserved charges Q_B and Q_c are the generators of the BRS transformation ond of the Faddeev-Popov ghost scale transformation, respectively. By clarifying the metric structures of the Fock space of asymptotic fields with help of the Ward-Takahashi identities, the physical S-matrix unitarity is established in just the same way as in the canonical theory of Yang-Mills fields.     

Entropy of a Black Hole with Distinct Surface Gravities

In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the WKB level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy and quantum creation of a black hole are also studied.     

On the ground state of Ising models with arbitrary spin quantum number

The ground state of a class of Ising models with site dependent arbitrary spin quantum number is shown to be restricted to ±S_i^MAX state where S_i^MAX is the spin quantum number at the site i.     

The quantum era

A universe is conceived as a gravitational quantum fluctuation stablized by coherent black hole creation out of expansion energy. The initial temperature is determined (T = 4.57 × 10¹⁶ GeV) and the adiabatic era causally explained. The theory has far-reaching implications for quantum gravity.     

Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

We consider U(n + 1) Yang–Mills instantons on the space Σ × S ², where Σ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on Σ × S ² are equivalent to non-Abelian vortex equations on Σ. Solutions to these equations are given by pairs (A,?), where A is a gauge potential of the group U(n) and ? is a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g > 1, when Σ × S ² becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.     

A compact rotating gravitational instanton

A compact rotating gravitational instanton (a positive-definite metric solution of the Einstein equations with Λ term) is presented. The manifold is the nontrivial S² fibre bundle over S² and has χ = 4, τ = 0, but no spinor structure. The metric can be obtained from a special limit of the positive-definite analytic extension of the Kerr-de Sitter metric or alternatively from the Taub-NUT metric with Λ term. The action is about $\text{4}\text{1}\text{2}\text{\%}$ less negative than that of the Einstein metric on the trivial bundle S² × S².     

S0 and S1 spectroscopy of jet cooled 9-cyano-10-methylanthracene: The methyl group as a molecular rotor

Jet-cooled fluorescence excitation and dispersed fluorescence spectra of 9-methylanthracene (MA), 9-cyanoanthracene (CA) and 9-cyano-10-methylanthracene (CMA) have been measured. The spectra of MA and CMA near the S₀-S₁ origin reveal a prominent torsional progression due to the hindered methyl group rotation and its torsional vibration against the aromatic ring frame. Additionally, the laser induced fluorescence LIF excitation spectrum of CMA shows the splitting of many vibrational modes.Observed positions and relative intensities of the methyl internal rotational bands were interpreted in terms of transitions calculated based on the quantum mechanical one-dimensional rotor. The low-frequency vibrational bands were interpreted also with the all electron quantum mechanical calculations within the RHF/6-31G(d,p), CIS/3-21G and CIS/6-31G(d,p) approximations. It is predicted that in the case of MA the eclipsed geometry (one C-H in the plane of the ring) is most stable in both S₀ and S₁ states. Conformation of the methyl group in CMA is suggested to change upon S₁ ← S₀ excitation (π/12 phase shift of the methyl group). The predicted energy barrier for methyl group rotation in the S₀ state of CMA is considerably higher (72 cm⁻¹) than that in the S₁ state (22 cm⁻¹). Following the present quantum mechanical calculations, the carbon atom of the methyl group belongs to the aromatic plane in the S₀ ground state but it deviates from this plane in the S₁ excited state. These in turn suggest that the calculated barrier for methyl group rotation in CMA has a 6-fold symmetry in the S₀ ground state and roughly a 4-fold symmetry in the S₁ state.     

Hydrogen atom and its energy level shifts in de Sitter universe

We investigate the influence of a cosmological constant on the energy levels of a one-electron atom in Fermi normal coordinates. The non-relativistic nS, nP energy levels and the relativistic 1S _1/2, 2S _1/2, 2P _1/2, 2P _3/2 energy levels are calculated in terms of the Riemann tensor. These energy level shifts are non-zero which indicate that the first order gravitational perturbations can partly remove the degeneracy of the studied states in de Sitter space. We show that it is not possible to use the hydrogen atom as a probe of background curvature of the universe. In the second order of perturbation, for 1S state, an upper limit for the energy shifts is obtained.     

(Non)-Abelian gauge field theories of the Fermi gas. Neutron-quark stars

It is indicated that the ground state of Fermi systems with (non)-Abelian gauge interactions has a well defined quantum theory devoid of infrared divergences and mass singularities. This is exploited to develop a systematic quantum theory of the quark gas. The equation of state of the quark gas is evaluated up to second order in the Gell-Mann-Low charge α_S(μ). The analysis based on neutron matter models suggests that the matter in the neutron stars can be in the quark phase provided the color interaction is “moderately” strong i.e. α_S (3 GeV) ? 0.3.     

Quantum correlations from classical Gaussian correlations

Already Schrödinger tried to proceed towards a purely wave theory of quantum phenomena. However, he should give up and accept Born’s probabilistic interpretation of the wave function. A simple mathematical fact was behind this crucial decision. The wave function of a composite system S = (S ₁, S ₂) belongs to the tensor product of two L2 spaces and not to their Cartesian product. It was impossible to consider it as a vector function ψ(x) = (ψ ₁(x), ψ ₂(x)), x ∈ R ³. Here we solved this problem. It is shown that there exists a mathematical formalism that provides a possibility to describe composite quantum systems without appealing to the tensor product of the Hilbert state space, and one can proceed with their Cartesian product. It may have important consequences for the understanding of entanglement and applications to quantum information theory. It seems that “quantum algorithms” can be realized on the basis of classical wave mechanics. However, the interpretation of the proposed mathematical formalism is a difficult problem and needs additional studies.