U(1) Connection, Nonlinear Dirac-like Equations and Seiberg-Witten Equations

By analysing the work of Campolattaro we argue that the second Seiberg-Witten equation over the Spin^c_4 manifold, i.e., F^+_{ij}=, is the generalization of the Campolattaro's description of the electromagnetic field tensor F^{\mu\nu} in the bilinear form F^{\mu\nu}=\bar{\Psi} S^{\mu\nu}\Psi. It turns out that the Seiberg-Witten equations (also the perturbed Seiberg-Witten equations) can be well understood from this point of view. We suggest that the second Seiberg-Witten equation can be replaced by a nonlinear Dirac-like Equation. We also derive the spinor representation of the connection on the associated unitary line bundle over the Spin^c_4 manifold.Comment: 10 page

Stochastic Gravity

We give a summary of the status of current research in stochastic semiclassical gravity and suggest directions for further investigations. This theory generalizes the semiclassical Einstein equation to an Einstein-Langevin equation with a stochastic source term arising from the fluctuations of the energy-momentum tensor of quantum fields. We mention recent efforts in applying this theory to the study of black hole fluctuations and backreaction problems, linear response of hot flat space, and structure formation in inflationary cosmology. To explore the physical meaning and implications of this stochastic regime in relation to both classical and quantum gravity, we find it useful to take the view that semiclassical gravity is mesoscopic physics and that general relativity is the hydrodynamic limit of certain spacetime quantum substructures. Three basic issues - stochasticity, collectivity, correlations- and three processes - dissipation, fluctuations, decoherence- underscore the transformation from quantum micro structure and interaction to the emergence of classical macro structure and dynamics. We discuss ways to probe into the high energy activity from below and make two suggestions: via effective field theory and the correlation hierarchy. We discuss how stochastic behavior at low energy in an effective theory and how correlation noise associated with coarse-grained higher correlation functions in an interacting quantum field could carry nontrivial information about the high energy sector. Finally we describe processes deemed important at the Planck scale, including tunneling and pair creation, wave scattering in random geometry, growth of fluctuations and forms, Planck scale resonance states, and spacetime foams.Comment: Latex 35 pages, to be published in Int. J. Theor. Phys. (1999

Nonequilibrium Quantum Fields in Cosmology: Comments on Selected Current Topics

Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for the analysis of quantum statistical processes in gravitation and cosmology. We raise a few conceptual questions and suggest some new directions of research on selected currrent topics on the physics of the early universe, such as entropy generation in cosmological particle creation, quantum theory of galaxy formation, and phase transition in inflationary cosmology.Comment: IASSNS-94/78, UMDPP-95-051, LATEX 16 pages (Invited Talk given at the Second Journee Cosmologie, Observatorie de Paris, June 2-4, 1994.

Fluctuation, Dissipation and Irreversibility in Cosmology

We discuss the appearance of time-asymmetric behavior in physical processes in cosmology and in the dynamics of the Universe itself. We begin with an analysis of the nature and origin of irreversibility in well-known physical processes such as dispersion, diffusion, dissipation and mixing, and make the distinction between processes whose irreversibility arises from the stipulation of special initial conditions, and those arising from the system's interaction with a coarse-grained environment. We then study the irreversibility associated with quantum fluctuations in cosmological processes like particle creation and the `birth of the Universe'. We suggest that the backreaction effect of such quantum processes can be understood as the manifestation of a fluctuation-dissipation relation relating fluctuations of quantum fields to dissipations in the dynamics of spacetime. For the same reason it is shown that dissipation is bound to appear in the dynamics of minisuperspace cosmologies. This provides a natural course for the emergence of a cosmological and thermodynamic arrow of time and suggests a meaningful definition of gravitational entropy. We conclude with a discussion on the criteria for the choice of coarse-grainings and the stability of persistent physical structures. Invited Talk given at the Conference on The Physical Origin of Time-Asymmetry Huelva, Spain, Oct. 1991, Proceedings eds. J. J. Halliwell, J. Perez-Mercader and W. H. Zurek, Cambridge University Press, 1993Comment: 31pp, UMDPP #93-5

A Kinetic Theory Approach to Quantum Gravity

We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).Comment: Latex 19 pages. Invited talk given at the 6th Peyresq Meeting, France, June, 2001. To appear in Int. J. Theor. Phys. 200

U(1) gauge theory over discrete space-time and phase transitions

We first apply Connes' noncommutative geometry to a finite point space. The explicit form of the action functional of U(1) gauge field on this n-point space is obtained. We then consider the case when the n-point space is replaced by {space-time}\times{n-point space}. This action is shown to relate the Hamiltonian of the continuous-spin formulation of the Potts model. We argue that U(1) gauge theory on the discrete space-time determines the geometric origin of a class of phase transitions.Comment: 12 page

Statistical Mechanics and Quantum Cosmology

Statistical mechanical concepts and processes such as decoherence, correlation, and dissipation can prove to be of basic importance to understanding some fundamental issues of quantum cosmology and theoretical physics such as the choice of initial states, quantum to classical transition and the emergence of time. Here we summarize our effort in 1) constructing a unified theoretical framework using techniques in interacting quantum field theory such as influence functional and coarse-grained effective action to discuss the interplay of noise, fluctuation, dissipation and decoherence; and 2) illustrating how these concepts when applied to quantum cosmology can alter the conventional views on some basic issues. Two questions we address are 1) the validity of minisuperspace truncation, which is usually assumed without proof in most discussions, and 2) the relevance of specific initial conditions, which is the prevailing view of the past decade. We also mention how some current ideas in chaotic dynamics, dissipative collective dynamics and complexity can alter our view of the quantum nature of the universe.Comment: Essay published in 1990 Conference Proceedings is reprinted here with no alteration nor reference update. It is antecedent to related reviews in gr-qc/9302025, gr-qc/9403061, gr-qc/951107

General Relativity as Geometro-Hydrodynamics

In the spirit of Sakharov's `metric elasticity' proposal, we draw a loose analogy between general relativity and the hydrodynamic state of a quantum gas. In the `top-down' approach, we examine the various conditions which underlie the transition from some candidate theory of quantum gravity to general relativity. Our emphasis here is more on the `bottom-up' approach, where one starts with the semiclassical theory of gravity and examines how it is modified by graviton and quantum field excitations near and above the Planck scale. We mention three aspects based on our recent findings: 1) Emergence of stochastic behavior of spacetime and matter fields depicted by an Einstein-Langevin equation. The backreaction of quantum fields on the classical background spacetime manifests as a fluctuation-dissipation relation. 2) Manifestation of stochastic behavior in effective theories below the threshold arising from excitations above. The implication for general relativity is that such Planckian effects, though exponentially suppressed, is in principle detectable at sub-Planckian energies. 3) Decoherence of correlation histories and quantum to classical transition. From Gell-Mann and Hartle's observation that the hydrodynamic variables which obey conservation laws are most readily decohered, one can, in the spirit of Wheeler, view the conserved Bianchi identity obeyed by the Einstein tensor as an indication that general relativity is a hydrodynamic theory of geometry. Many outstanding issues surrounding the transition to general relativity are of a nature similar to hydrodynamics and mesoscopic physics.Comment: Latex 18 pages. Expanded version of an invited talk given at the Second Sakharov International Symposium, Lebedev Physical Institute, Moscow, May 20-24, 199

Can Spacetime be a Condensate?

We explore further the proposal that general relativity is the hydrodynamic limit of some fundamental theories of the microscopic structure of spacetime and matter, i.e., spacetime described by a differentiable manifold is an emergent entity and the metric or connection forms are collective variables valid only at the low energy, long wavelength limit of such micro-theories. In this view it is more relevant to find ways to deduce the microscopic ingredients of spacetime and matter from their macroscopic attributes than to find ways to quantize general relativity because it would only give us the equivalent of phonon physics, not the equivalents of atoms or quantum electrodyanmics. It may turn out that spacetime is merely a representation of collective state of matter in some limiting regime of interactions, which is the view expressed by Sakharov. In this talk, working within the conceptual framework of geometro-hydrodynamics, we suggest a new way to look at the nature of spacetime inspired by Bose-Einstein Condensate (BEC) physics. We ask the question whether spacetime could be a condensate, even without the knowledge of what the `atom of spacetime' is. We begin with a summary of the main themes for this new interpretation of cosmology and spacetime physics, and the `bottom-up' approach to quantum gravity. We then describe the `Bosenova' experiment of controlled collapse of a BEC and our cosmology-inspired interpretation of its results. We discuss the meaning of a condensate in different context. We explore how far this idea can sustain, its advantages and pitfalls, and its implications on the basic tenets of physics and existing programs of quantum gravity.Comment: 12 pages Latex. Added some references and footnotes pertaining to work of authors on related theme

Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schr\"odinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.Comment: 18 pages. Invited talk at the Second International Conference on Emergent Quantum Mechanics, Vienna, October 3-6, 2013. Note: this arXiv version is more up to date than that which will appear in J. Phys. (Conf. Ser.