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Lee Smolin

Publications and source records attributed to Lee Smolin.

At least 145 records · Page 8Linked to original sources
arXiv1998

Chern-Simons theory in 11 dimensions as a non-perturbative phase of M theory

A Chern-Simons theory in 11 dimensions, which is a piece of the 11 dimensional supergravity action, is considered as a quantum field theory in its own right. We conjecture that it defines a non-perturbative phase of M theory in which the metric and gravitino vanish. The theory is diffeomorphism invariant but not topological in that there are local degrees of freedom. Nevertheless, there are a countable number of momentum variables associated with relative cobordism classes of embeddings of seven dimensional manifolds in ten dimensional space. The canonical theory is developed in terms of an algebra of gauge invariant observables. We find a sector of the theory corresponding to a topological compactification in which the geometry of the compactified directions is coded in an algebra of functions on the base manifold. The diffeomorphism invariant quantum theory associated to this sector is constructed, and is found to describe diffeomorphism classes of excitations of three surfaces wrapping homology classes of the compactified dimensions.

hep-th↗
arXiv1998

Strings as perturbations of evolving spin-networks

A connection between non-perturbative formulations of quantum gravity and perturbative string theory is exhibited, based on a formulation of the non-perturbative dynamics due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) is extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory.

hep-th↗
arXiv1998

Nonperturbative dynamics for abstract (p,q) string networks

We describe abstract (p,q) string networks which are the string networks of Sen without the information about their embedding in a background spacetime. The non-perturbative dynamical formulation invented for spin networks, in terms of causal evolution of dual triangulations, is applied to them. The formal transition amplitudes are sums over discrete causal histories that evolve (p,q) string networks. The dynamics depend on two free SL(2,Z) invariant functions which describe the amplitudes for the local evolution moves.

hep-th↗
arXiv1997

Quantum geometry with intrinsic local causality

The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group G_q over all compact (finite genus) oriented 2-surfaces. The dynamics is background independent and locally causal. The dynamics constructs histories with discrete features of spacetime geometry such as causal structure and multifingered time. For SU(2) the theory satisfies the Bekenstein bound and the holographic hypothesis is recast in this formalism.

gr-qc↗
arXiv1997

Covariant quantization of membrane dynamics

A Lorentz covariant quantization of membrane dynamics is defined, which also leaves unbroken the full three dimensional diffeomorphism invariance of the membrane. Among the applications studied are the reduction to string theory, which may be understood in terms of the phase space and constraints, and the interpretation of physical,zero-energy states. A matrix regularization is defined as in the light cone gauged fixed theory but there are difficulties implementing all the gauge symmetries. The problem involves the non-area-preserving diffeomorphisms which are realized non-linearly in the classical theory. In the quantum theory they do not seem to have a consistent implementation for finite N. Finally, an approach to a genuinely background independent formulation of matrix dynamics is briefly described.

hep-th↗
arXiv1997

A possible solution to the problem of time in quantum cosmology

We argue that in classical and quantum theories of gravity the configuration space and Hilbert space may not be constructible through any finite procedure. If this is the case then the "problem of time" in quantum cosmology may be a pseudo-problem, because the argument that time disappears from the theory depends on constructions that cannot be realized by any finite beings that live in the universe. We propose an alternative formulation of quantum cosmological theories in which it is only necessary to predict the amplitudes for any given state to evolve to a finite number of possible successor states. The space of accessible states of the system is then constructed as the universe evolves from any initial state. In this kind of formulation of quantum cosmology time and causality are built in at the fundamental level. An example of such a theory is the recent path integral formulation of quantum gravity of Markopoulou and Smolin, but there are a wide class of theories of this type.

gr-qc↗
arXiv1997

The future of spin networks

The roles that spin networks play in gauge theories, quantum gravity and topological quantum field theory are briefly described, with an emphasis on the question of the relationships among them. It is argued that spin networks and their generalizations provide a language which may lead to a unification of the different approaches to quantum gravity and quantum geometry. This leads to a set of conjectures about the form of a future theory that may be simultaneously an extension of the non-perturbative quantization of general relativity and a non-perturbative formulation of string theory.

gr-qc↗
arXiv1997

Causal evolution of spin networks

A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal sets, which consist of spin networks representing quantum states of the gravitational field joined together by labeled null edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also be interepreted as a theory of labeled timelike surfaces. The dynamics is specified by a choice of functions of the labelings of d+1 dimensional simplices,which represent elementary future light cones of events in these discrete spacetimes. The quantum dynamics thus respects the discrete causal structure of the causal sets. In the 1+1 dimensional case the theory is closely related to directed percolation models. In this case, at least, the theory may have critical behavior associated with percolation, leading to the existence of a classical limit.

gr-qc↗
arXiv1996

Galactic disks as reaction-diffusion systems

A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the development of inhomogeneities, leading to the development of spatial and temporal structure. At the linearized level a prediction for the length and time scales of the patterns is found. These instabilities arise for the same reason that pattern formation is seen in non-equilibrium chemical and biological systems, which is that the positive and negative feedback effects which govern the rates of the critical processes act over different distance scales, as in Turing's reaction-diffusion models. This shows that patterns would form in the disk even in the absence of gravitational effects, density waves, rotation, shear and external perturbations. These nonlinear effects may thus explain the spiral structure seen in the star forming regions of isolated flocculent galaxies.

astro-ph↗
arXiv1996

Three Dimensional Strings as Collective Coordinates of Four Dimensional Non-Perturbative Quantum Gravity

A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric emerge as collective coordinates that describe a sector of the solution space of quantum general relativity. Additional collective coordinates exist which are interpreted as worldsheet degrees of freedom. The construction may be extended to the case in which the Kalb-Ramond field is included in the non-perturbative dynamics. It is possible that this mechanism is the inverse of the strong coupling limit by which some $D$ dimensional string theories are conjectured to give rise to $D+1$ dimensional field theories.

gr-qc↗
arXiv1996

The classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity

It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because the form of the state allows a division into spatial regions, such that no change in the physical state in one region can be measured by observables restricted to another. These disconnected regions have generically finite expectation value of physical volume, which means that the theory has no long ranged correlations or massless particles. One consequence of this is that the $ADM$ energy is unbounded from below, at least when that is defined with respect to a natural notion of quantum asymptotic flatness and a corresponding definition of an operator that measures $E_{ADM}$ (which is given here). These problems occur in Thiemann's new formulation of quantum gravity. Related issues arise in some other approaches such as that of Borissov, Rovelli and Smolin. A new approach to the Hamiltonian constraint, which may avoid the problem of the lack of long ranged correlations, is proposed.

gr-qc↗
arXiv1996

Mixmaster quantum cosmology in terms of physical dynamics

An approach to quantum cosmology, relying on strengths of both canonical and path integral formalisms, is applied to the cosmological model, Bianchi type IX. Physical quantum states are constructed on the maximal slice of the cosmological history. A path integral is derived which evolves observables off the maximal slice. This result is compared a path integral propagator derived earlier with conventional Faddeev-Poppov gauge fixing.

gr-qc↗
arXiv1996

Experimental Signatures of Quantum Gravity

I review several different calculations, coming from string theory, nonperturbative quantum gravity and analyses of black holes that lead to predictions of phenomena that would uniquely be signatures of quantum gravitational effects. These include: 1) deviations from a thermal spectra for evaporating black holes, 2) upper limits on the entropy and energy content of bounded regions, 3) suppression of ultra-high energy scattering amplitudes, consistent with a modified uncertainty principle, 4) physical volumes and areas have discrete spectra, 5), violations of $CPT$ and universal violations of $CP$, 6) otherwise inexplicable conditions on the initial state of the universe or otherwise inexplicable correlations between cosmological and microscopic parameters. Consideration of all of these together suggests the possibility of connections between perturbative and nonperturbative approaches to quantum gravity.

gr-qc↗
arXiv1996

Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity

Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the boundary is self-dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all $SU(2)$ Chern-Simon theories defined by all choices of punctures and representations on the spatial boundary $\cal S$. The integer level $k$ of Chern-Simons theory is found to be given by $k= 6π/G^2 Λ+ α$, where $Λ$ is the cosmological constant and $α$ is a $CP$ breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. The Beckenstein bound and 't Hooft-Susskind holographic hypothesis are confirmed, (in the limit of large area and small cosmological constant) in the sense that once the two metric of the boundary has been measured, the subspace of the physical state space that describes the further information that the observer on the boundary may obtain about the interior has finite dimension equal to the exponent of the area of the boundary, in Planck units, times a fixed constant. Finally,the construction of the state space for quantum gravity in a region from that of all Chern-Simon theories defined on its boundary confirms the categorical-theoretic ``ladder of dimensions picture" of Crane.

gr-qc↗
arXiv1995

The geometry of quantum spin networks

The discrete picture of geometry arising from the loop representation of quantum gravity can be extended by a quantum deformation. The operators for area and volume defined in the q-deformation of the theory are partly diagonalized. The eigenstates are expressed in terms of q-deformed spin networks. The q-deformation breaks some of the degeneracy of the volume operator so that trivalent spin-networks have non-zero volume. These computations are facilitated by use of a technique based on the recoupling theory of SU(2)_q, which simplifies the construction of these and other operators through diffeomorphism invariant regularization procedures.

gr-qc↗
arXiv1995

Quantum deformation of quantum gravity

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum gravity characterized by states which are normalizable in the measure of Chern-Simons theory. The deformation parameter, q, depends on the cosmological constant. The Mandelstam identities are extended to a set of relations which are governed by the Kauffman bracket so that the spin network basis is deformed to a basis of SU(2)q spin networks. Corrections to the actions of operators in non-perturbative quantum gravity may be readily computed using recoupling theory; the example of the area observable is treated here. Finally, eigenstates of the q-deformed Wilson loops are constructed, which may make possible the construction of a q-deformed connection representation through an inverse transform.

gr-qc↗
arXiv1995

The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field Theory

An approach to quantum gravity and cosmology is proposed based on a synthesis of four elements: 1) the Bekenstein bound and the related holographic hypothesis of 't Hooft and Susskind, 2) topological quantum field theory, 3) a new approach to the interpretational issues of quantum cosmology and 4) the loop representation formulation of non-perturbative quantum gravity. A set of postulates are described, which define a (\it pluralistic quantum cosmological theory.) These incorporates a statistical and relational approach to the interpretation problem, following proposals of Crane and Rovelli, in which there is a Hilbert space associated to each timelike boundary, dividing the universe into two parts. A quantum state of the universe is an assignment of a statistical state into each of these Hilbert spaces, subject to certain conditions of consistency which come from an analysis of the measurement problem. A proposal for a concrete realization of these postulates is described, which is based on certain results in the loop representation and topological quantum field theory, and in particular on the fact that spin networks and punctured surfaces appear in both contexts. The Capovilla-Dell-Jacobson solution of the constraints of quantum gravity are expressed quantum mechanically in the language of Chern-Simons theory, in a way that leads also to the satisfaction of the Bekenstein bound.

gr-qc↗