Quantum poincaré group for isotropic quantum space-time

Possibilities of isotropic deformation of space-time are studied. The result is the two-parameter deformation. A differential calculus on the quantum space-time is constructed and the quantum differential geometry is formulated. A group of rigid motion of quantum space-time is investigated. This group is an example of a quantized braided group.     

Stationary states in a quantum gravity model

A model theory for quantized gravity is discussed where only selected degrees of freedom are quantized. The concept of stationary states is introduced. It is shown that the Planck length arises as a lower bound to the space-time length scale in a natural way.     

A new approach to the theory of elementary domains

It is shown that Yukawa's theory of elementary domains can be formulated in a general framework. A quantized measure space structure of a space-time manifold is introduced so as to represent faithfully the elementary-domain structure. For a realization of elementary domains, an operator valued measure is defined such that it represents the spatiotemporal distribution of elementary domains. Effects of such a quantized topology are illustrated in the expressions ofS matrices.     

Universal measurement of quantum correlations of radiation

A measurement technique is proposed which, in principle, allows one to observe the general space-time correlation properties of a quantized radiation field. Our method, called balanced homodyne correlation measurement, unifies the advantages of balanced homodyne detection with those of homodyne correlation measurements.     

Discrete Space-Time and Lorentz Symmetry

Recent observations of Ultra High Energy Cosmic rays suggest a small violation of Lorentz symmetry. Such a violation is expected in schemes with discrete/quantized space-time. We examine this situation and suggest tests which could be carried out by, for example NASA's forthcoming GLAST Satellite.     

The vanishing likelihood of space-time singularity in quantum conformal cosmology

A general formalism is developed for studying the behavior of quantized conformal fluctuations near the space-time singularity of classical relativistic cosmology. It is shown that if the material contents of space-time are made of massive particles which obey the principle of asymptotic freedom and interact only gravitationally, then it is possible to estimate the quantum mechanical probability that, of the various possible conformal transforms of the classical Einstein solution, the actual model had a singularity in the past. This probability turns out to be vanishingly small, thus indicating that within the regime of quantum conformal cosmology it is extremely unlikely that the universe originated out of a space-time singularity.     

Space-Time Curvature Induced by Quantum Vacuum Fluctuations as an Alternative to Dark Energy

It is shown that quantum vacuum fluctuations give rise to a curvature of space-time of the order appropriate to explain the observed accelerated expansion of the universe. The fact that the fluctuations produce curvature, even if the expectation of the vacuum energy vanishes, is a consequence of the non-linear character of the Einstein equation. A calculation is made, involving plausible hypotheses within quantized gravity, which establishes a relation between the two-point correlation of the vacuum fluctuations and the space-time curvature.     

Open quantum system approach to the Gibbons-Hawking effect of de Sitter space-time

We analyze, in the paradigm of open quantum systems, the reduced dynamics of a freely falling two-level detector in de Sitter space-time in weak interaction with a reservoir of fluctuating quantized conformal scalar fields in the de Sitter-invariant vacuum. We find that the detector is asymptotically driven to a thermal state at the Gibbons-Hawking temperature, regardless of its initial state. Our discussion, therefore, shows that the Gibbons-Hawking effect of de Sitter space-time can be understood as a manifestation of thermalization phenomena that involves decoherence and dissipation in open quantum systems.     

Quantized De Sitter space,the connection to the Pauli principle and an application to Feynman's relativistic quark theory II

A continuation of a previous paper, in which a model of a quantized space-time theory has been investigated, considers further problems of a quantized De Sitter space. There will be shown that a De Sitter space is a very useful starting point to a non-local relativistic quantum field theory, containing the Pauli principle, for the theory of elementary particles, as a connection to Feynman's relativistic quark theory, where the groupSU(3) has a particular importance, will be discussed. This method offers the possibility of treating weak local differences from a space with De Sitter metric as a perturbation. Therefore the problem of a fundamental elementary lengthl _o must be considered in connection with the general theory of relativity.     

Normalization of Quantized Area Using Torsion and Spin

We calculate the change in physical space-time area associated with defects in space-time due to torsion when a particle with spin is present. This change in area is then set equal to the component of the quantized area due to a link of color P_l in the spin network originally calculated by Rovelli and Smolin [6] and shown to have an arbitrary constant factor, the Immirzi parameter, by several authors. Using the usual quantization condition for the square of the spin then allows us to calculate this arbitrary constant factor. We find a well defined expression for the quantized area, . An interesting picture emerges where a missing link of color P_l in the spin network looks like a torsional defect in space-time associated with a particle of spin j_l = P_l/ 2.     

Stress Tensor Fluctuations and Passive Quantum Gravity

The quantum fluctuations of the stress tensor of a quantum field are discussed, as are the resulting space-time metric fluctuations. Passive quantum gravity is an approximation in which gravity is not directly quantized, but fluctuations of the space-time geometry are driven by stress tensor fluctuations. We discuss a decomposition of the stress tensor correlation function into three parts, and consider the physical implications of each part. The operational significance of metric fluctuations and the possible limits of validity of semiclassical gravity are discussed.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

Geometric quantization of topological gauge theories

We show that Abelian gauge theories in 2+1 space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case.     

Quantum conformal fluctuations near the classical space-time singularity

This paper investigates the behavior of conformal fluctuations of space-time geometry that are admissible under the quantized version of Einstein's general relativity. The approach to quantum gravity is via path integrals. It is shown that considerable simplification results when only the conformal degrees of freedom are considered under this scheme, so much so that it is possible to write down a formal kernel in the most general case where the space-time contains arbitrary distributions of particles with no other interaction except gravity. The behavior of this kernel near the classical space-time singularity then shows that quantum fluctuations inevitably diverge near the singularity. It is shown further that the root cause of this divergence lies in the fact that the Green's function for the conformally invariant scalar wave equation diverges at the singularity. The limitations on the validity of classical general relativity near the space-time singularity are discussed and it is argued that the notion of singularity itself needs to be radically modified once the quantum effects are taken into account.On leave of absence from the Tata Institute of Fundamental Research, Bombay, India     

Finite-dimensional relativistic quantum mechanics

A finite-dimensional relativistic quantum mechanics is developed by first quantizing Minkowski space. Two-dimensional space-time event observables are defined and quantum microscopic causality is studied. Three-dimensional colored even observables are introduced and second quantized on a representation space of the restricted Poincaré group. Creation, annihilation, and field operators are introduced and a finite-dimensional Dirac theory is presented.     

Quantized space-time and its influence on two physical problems

Based on Snyder's idea of quantized space-time, we derive a new generalized uncertainty principle and new modified density of states. Accordingly, we discuss the influence of the modified generalized uncertainty principle on the black hole entropy and the influence of the modified density of states on the Stefan-Boltzman law.     

Gravitational and quantum effects in rotating cosmological models

Specific effects of the dynamics of (spinor and scalar) wave fields are considered in rotating uniform Gödel-type cosmological models. It is shown that the gravitational interaction of the spinor field can be reduced to the interaction between its pseudovector current and the angular velocity of space-time rotation and is similar to its interaction with the pseudotrace of the space-time twisting. The mean values of energy-momentum tensor of the quantized scalar field in vacuum are calculated in rotating cosmological models and the difference between these values and their mean counterparts in vacuum is determined for Friedman's nonrotating cosmological models.State Education Institute, Yaroslavl'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–38, June, 1992.     

Condensation and evolution of a space-time network

In this work, we try to propose in a novel way, using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of a space-time network described by the Loop quantum gravity. Considering quantum network connectivity features in Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of the quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induces a huge curved space-time network may indicate space time condensation in high-energy nodes. For example, in the case of black holes, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to the quantum number of the area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for the space-time network is quantized, which can form space-time network condensation. The black hole is a sort of result of space-time network condensation, however there may be more extensive space-time network condensations, such as the universe singularity (big bang).      

Definition of the vacuum in curved space-time

It is proposed that the vacuum state of quantized fields in curved space-time be defined as the state which minimizes the average value of the field Hamiltonian. Starting from this definition, equations are obtained for finding positive- and negative-frequency functions for spinor and scalar fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 16–21, July, 1979.