133,110 research outputs found
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
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
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
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.
Decoherence of Two-Level Systems Can Be Very Different From Brownian Particles
In quantum computation, it is of paramount importance to locate the parameter
space where maximal coherence can be preserved in the qubit system. In recent
years environment-induced decoherence based the quantum Brownian motion (QBM)
models have been applied to two level systems (2LS) interacting with an
electromagnetic field, leading to the general belief that 2LS are easily
decohered. In a recent paper C. Anastopoulos and B. L. Hu [Phys. Rev. A62,
(2000) 033821] derived a new exact non-Markovian master equation at zero
temperature, from which they showed that this belief is actually misplaced. For
a two-level atom (2LA)- electromagnetic field (EMF) system the decoherence time
is rather long, comparable to the relaxation time. Theoretically this is
because the dominant interaction is the type of coupling
between the two levels (what constitutes the qubit) and the field, not the
type, which shows the QBM behavior. Depending on the coupling
the field can act as a resonator (in an atom cavity) or as a bath (in QBM) and
produce very different decoherent behavior in the system. This is not new to
Cavity QED experimentalists: the 2LA-EMF system maintaining its coherence in
sufficiently long duration is the reason why they can manipulate them so well
to show interesting quantum coherence effects.Comment: Latex 15 pages Invited talk given at the Workshop on Mechanisms of
Decoherence, University of Texas, Austin. Oct. 2001 Summary of PRA (2000)
paper with Charis Anastopoulo
Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
We explore in stochastic gravity theory whether non-Gaussian noises from the
higher order correlation functions of the stress tensor for quantum matter
fields when back-reacting on the spacetime may reveal hints of multi-scale
structures. Anomalous diffusion may depict how a test particle experiences in a
fractal spacetime. The hierarchy of correlations in quantum matter field
induces the hierarchy of correlations in geometric objects via the set of
Einstein-Langevin equations for each correlation order. This correlation
hierarchy kinetic theory conceptual framework, aided by the characteristics of
stochastic processes, may serve as a conduit for connecting the low energy
`Bottom-Up' approach with the `Top-Down' theories of quantum gravity which
predict the appearance of fractal spacetimes at the Planck scale.Comment: 16 pages. Invited talk at DICE2016 conference: "Spacetime - Matter -
Quantum Mechanics", September 201
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