4,809 research outputs found
Towards the Unification of Gravity and other Interactions: What has been Missed?
Faced with the persisting problem of the unification of gravity with other
fundamental interactions we investigate the possibility of a new paradigm,
according to which the basic space of physics is a multidimensional space
associated with matter configurations. We consider general
relativity in . In spacetime, which is a 4-dimensional subspace of
, we have not only the 4-dimensional gravity, but also other
interactions, just as in Kaluza-Klein theories. We then consider a finite
dimensional description of extended objects in terms of the center of mass,
area, and volume degrees of freedom, which altogether form a 16-dimensional
manifold whose tangent space at any point is Clifford algebra Cl(1,3). The
latter algebra is very promising for the unification, and it provides
description of fermions.Comment: 11 pages; Talk presented at "First Mediterranean Conference on
Classical and Quantum Gravity", Kolymbari, Crete, Greece, 14-18 September
200
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
The geometry of the Barbour-Bertotti theories I. The reduction process
The dynamics of interacting particles is investigated in the
non-relativistic context of the Barbour-Bertotti theories. The reduction
process on this constrained system yields a Lagrangian in the form of a
Riemannian line element. The involved metric, degenerate in the flat
configuration space, is the first fundamental form of the space of orbits of
translations and rotations (the Leibniz group). The Riemann tensor and the
scalar curvature are computed by a generalized Gauss formula in terms of the
vorticity tensors of generators of the rotations. The curvature scalar is
further given in terms of the principal moments of inertia of the system. Line
configurations are singular for . A comparison with similar methods in
molecular dynamics is traced.Comment: 15 pages, to appear in Classical and Quantum Gravit
Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical Potential
We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density
(chemical potential mu =/= 0). It is possible to formulate this model with a
real action and therefore to perform standard hybrid Monte Carlo simulations
with mu =/= 0 in the functional measure. We compare the physical observables
from these simulations with simulations using the Glasgow method where the
value of mu in the functional measure is fixed at a value mu_upd. We find that
the observables are sensitive to the choice of mu_upd. We consider the
implications of our findings for Glasgow method QCD simulations at mu =/= 0. We
demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu
model is fundamentally different from that in QCD. We find that this difference
explains why there is an unphysical transition in QCD simulations at mu =/= 0
associated with the pion mass scale whereas the transition in the Gross-Neveu
model occurs at a larger mass scale and is therefore consistent with
theoretical predictions. We note classes of theories which are exceptions to
the Vafa-Witten theorem which permit the possibility of formation of baryon
number violating diquark condensates.Comment: 28 pages RevTe
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
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.Comment: Latex, 21 pages, no figure
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general
relativity that does not require a Lorentz invariant spacetime. Instead, we
find that gravity admits a dual description in terms of a theory where local
size is irrelevant. The dual theory is invariant under foliation preserving
3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume
(for the spatially compact case). Locally, this symmetry is identical to that
of Horava-Lifshitz gravity in the high energy limit but our theory is
equivalent to Einstein gravity. Specifically, we find that the solutions of
general relativity, in a gauge where the spatial hypersurfaces have constant
mean extrinsic curvature, can be mapped to solutions of a particular gauge
fixing of the dual theory. Moreover, this duality is not accidental. We provide
a general geometric picture for our procedure that allows us to trade foliation
invariance for conformal invariance. The dual theory provides a new proposal
for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections
New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
I show how there is an ambiguity in how one treats auxiliary variables in
gauge theories including general relativity cast as 3 + 1 geometrodynamics.
Auxiliary variables may be treated pre-variationally as multiplier coordinates
or as the velocities corresponding to cyclic coordinates. The latter treatment
works through the physical meaninglessness of auxiliary variables' values
applying also to the end points (or end spatial hypersurfaces) of the
variation, so that these are free rather than fixed. [This is also known as
variation with natural boundary conditions.] Further principles of dynamics
workings such as Routhian reduction and the Dirac procedure are shown to have
parallel counterparts for this new formalism. One advantage of the new scheme
is that the corresponding actions are more manifestly relational. While the
electric potential is usually regarded as a multiplier coordinate and Arnowitt,
Deser and Misner have regarded the lapse and shift likewise, this paper's
scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose
corresponding velocities are, respectively, the abovementioned previously used
variables. This paper's way of thinking about gauge theory furthermore admits
interesting generalizations, which shall be provided in a second paper.Comment: 11 page
Results on Finite Density QCD
A brief summary of the formulation of QCD at finite chemical potental, ,
is presented. The failure of the quenched approximation to the problem is
reviewed.
Results are presented for dynamical simulations of the theory at strong and
intermediate couplings. We find that the problems associated with the quenched
theory persist: the onset of non-zero quark number does seem to occur at a
chemical potential . However analysis of the
Lee-Yang zeros of the grand canonical partition function in the complex
fugacity plane, (), does show signals of critical behaviour in the
expected region of chemical potential.
Results are presented for a simulation at finite density of the Gross-Neveu
model on a lattice near to the chiral limit. Contrary to our simulations
of QCD no pathologies were found when passed through the value
m_{\pi}/2}.Comment: 14 pages, Latex, 18 eps figures, Review for Tsukuba worksho
Alien Registration- Elliott, Lola B. (Bath, Sagadahoc County)
https://digitalmaine.com/alien_docs/9517/thumbnail.jp
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