140 research outputs found
Square Root Actions, Metric Signature, and the Path-Integral of Quantum Gravity
We consider quantization of the Baierlein-Sharp-Wheeler form of the
gravitational action, in which the lapse function is determined from the
Hamiltonian constraint. This action has a square root form, analogous to the
actions of the relativistic particle and Nambu string. We argue that
path-integral quantization of the gravitational action should be based on a
path integrand rather than the familiar Feynman expression
, and that unitarity requires integration over manifolds of both
Euclidean and Lorentzian signature. We discuss the relation of this path
integral to our previous considerations regarding the problem of time, and
extend our approach to include fermions.Comment: 32 pages, latex. The revision is a more general treatment of the
regulator. Local constraints are now derived from a requirement of regulator
independenc
k-String tensions and the 1/N expansion
We address the question of whether the large-N expansion in pure SU(N) gauge
theories requires that k-string tensions must have a power series expansion in
1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as
in Casimir scaling. We find that k-string tensions may, in fact, have 1/N
corrections, and consistency with the large-N expansion in the open-string
sector depends crucially on an exact cancellation, which we will prove, among
terms involving odd powers of 1/N in particular combinations of Wilson loops.
It is shown how these cancellations are fulfilled, and consistency with the
large-N expansion achieved, in a concrete example, namely, strong-coupling
lattice gauge theory with the heat-kernel action. This is a model which has
both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis
of the closed string channel in this model confirms our conclusions, and
provides further insights into the large-N dependence of energy eigenstates and
eigenvalues.Comment: RevTeX4, 21 pages. Typos corrected, references added, some
discussions expanded; conclusions unchanged. Version to appear on PR
Center Dominance in SU(2) Gauge-Higgs Theory
We study the SU(2) gauge-Higgs system in D=4 dimensions, and analyze the
influence of the fundamental-representation Higgs field on the vortex content
of the gauge field. It is shown that center projected Polyakov lines, at low
temperature, are finite in the infinite volume limit, which means that the
center vortex distribution is consistent with color screening. In addition we
confirm and further investigate the presence of a "Kertesz-line" in the
strong-coupling region of the phase diagram, which we relate to the percolation
properties of center vortices. It is shown that this Kertesz-line separates the
gauge-Higgs phase diagram into two regions: a confinement-like region, in which
center vortices percolate, and a Higgs region, in which they do not. The free
energy of the gauge-Higgs system, however, is analytic across the Kertesz line.Comment: 7 pages, 10 figure
Wilson loops in four-dimensional quantum gravity
A Wilson loop is defined, in 4-D pure Einstein gravity, as the trace of the
holonomy of the Christoffel connection or of the spin connection, and its
invariance under the symmetry transformations of the action is showed
(diffeomorphisms and local Lorentz transformations). We then compute the loop
perturbatively, both on a flat background and in the presence of an external
source; we also allow some modifications in the form of the action, and test
the action of ``stabilized'' gravity. A geometrical analysis of the results in
terms of the gauge group of the euclidean theory, , leads us to the
conclusion that the correspondent statistical system does not develope any
configuration with localized curvature at low temperature. This ``non-local''
behavior of the quantized gravitational field strongly contrasts with that of
usual gauge fields. Our results also provide an explanation for the absence of
any invariant correlation of the curvature in the same approximation.Comment: 19 pages, LaTex, report CTP #2225, June 199
A novel probe of the vacuum of the lattice gluodynamics
We introduce a notion of minimal number of negative links on the lattice for
a given original configuration of SU(2) fields. Negative links correspond to a
large potential, not necessarily large action. The idea is that the minimal
number of negative links is a gauge invariant notion. To check this hypothesis
we measure correlator of two negative links, averaged over all the directions,
as function of the distance between the links. The inverse correlation length
coincides within the error bars with the lightest glueball mass.Comment: 6 pages, 2 figure
A variational approach to the QCD wave functional:Dynamical mass generation and confinement
We perform a variational calculation in the SU(N) Yang Mills theory in 3+1
dimensions. Our trial variational states are explicitly gauge invariant, and
reduce to simple Gaussian states in the zero coupling limit. Our main result is
that the energy is minimized for the value of the variational parameter away
form the perturbative value. The best variational state is therefore
characterized by a dynamically generated mass scale . This scale is related
to the perturbative scale by the following relation:
. Taking the one loop QCD -
function and we find (for N=3) the vacuum condensate
.Comment: 37 pages, (1 Figure available upon request), preprint LA-UR-94-2727,
PUPT-149
Fundamental Constants and the Problem of Time
We point out that for a large class of parametrized theories, there is a
constant in the constrained Hamiltonian which drops out of the classical
equations of motion in configuration space. Examples include the mass of a
relativistic particle in free fall, the tension of the Nambu string, and
Newton's constant for the case of pure gravity uncoupled to matter or other
fields. In the general case, the classically irrelevant constant is
proportional to the ratio of the kinetic and potential terms in the
Hamiltonian. It is shown that this ratio can be reinterpreted as an {\it
unconstrained} Hamiltonian, which generates the usual classical equations of
motion. At the quantum level, this immediately suggests a resolution of the
"problem of time" in quantum gravity. We then make contact with a recently
proposed transfer matrix formulation of quantum gravity and discuss the
semiclassical limit. In this formulation, it is argued that a physical state
can obey a (generalized) Poincar\'e algebra of constraints, and still be an
approximate eigenstate of 3-geometry. Solutions of the quantum evolution
equations for certain minisuperspace examples are presented. An implication of
our proposal is the existence of a small, inherent uncertainty in the
phenomenological value of Planck's constant.Comment: 46 pages + 5 figures, LaTex, NBI-HE-94-3
Dynamical Determination of the Metric Signature in Spacetime of Nontrivial Topology
The formalism of Greensite for treating the spacetime signature as a
dynamical degree of freedom induced by quantum fields is considered for
spacetimes with nontrivial topology of the kind , for varying . It is shown that a dynamical origin for the Lorentzian
signature is possible in the five-dimensional space with small torus radius (periodic boundary conditions), as well as in
four-dimensional space with trivial topology. Hence, the possibility exists
that the early universe might have been of the Kaluza-Klein type, \ie
multidimensional and of Lorentzian signature.Comment: 10 pages, LaTeX file, 4 figure
Complex lapse, complex action and path integrals
Imaginary time is often used in quantum tunnelling calculations. This article
advocates a conceptually sounder alternative: complex lapse. In the ``3+1''
action for the Einstein gravitational field minimally coupled to a Klein-Gordon
field, allowing the lapse function to be complex yields a complex action which
generates both the usual Lorentzian theory and its Riemannian analogue, and in
particular allows a change of signature between the two. The action and
variational equations are manifestly well defined in the Hamiltonian
representation, with the momentum fields consequently being complex. The
complex action interpolates between the Lorentzian and Riemannian actions as
they appear formally in the respective path integrals. Thus the complex-lapse
theory provides a unified basis for a path-integral quantum theory of gravity
involving both Lorentzian and Riemannian aspects. A major motivation is the
quantum-tunnelling scenario for the origin of the universe. Taken as an
explanation for the observed quantum tunnelling of particles, the complex-lapse
theory determines that the argument of the lapse for the universe now is
extremely small but negative.Comment: 12 pages, Te
Wilson Loop, Regge Trajectory and Hadron Masses in a Yang-Mills Theory from Semiclassical Strings
We compute the one-loop string corrections to the Wilson loop, glueball Regge
trajectory and stringy hadron masses in the Witten model of non supersymmetric,
large-N Yang-Mills theory. The classical string configurations corresponding to
the above field theory objects are respectively: open straight strings, folded
closed spinning strings, and strings orbiting in the internal part of the
supergravity background. For the rectangular Wilson loop we show that besides
the standard Luescher term, string corrections provide a rescaling of the field
theory string tension. The one-loop corrections to the linear glueball Regge
trajectories render them nonlinear with a positive intercept, as in the
experimental soft Pomeron trajectory. Strings orbiting in the internal space
predict a spectrum of hadronic-like states charged under global flavor
symmetries which falls in the same universality class of other confining
models.Comment: 52 pages, latex 3 times, v3: references adde
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