1,227 research outputs found
Variational formulation of Eisenhart's unified theory
Eisenhart's classical unified field theory is based on a non-Riemannian
affine connection related to the covariant derivative of the electromagnetic
field tensor. The sourceless field equations of this theory arise from
vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate
Eisenhart's theory from the metric-affine variational principle. In this
formulation, a Lagrange multiplier constraining the torsion becomes the source
for the Maxwell equations.Comment: 7 pages; published versio
New results for the missing quantum numbers labeling the quadrupole and octupole boson basis
The many -pole boson states, with ,
realize the irreducible representation (IR) for the group reduction chains
. They have been analytically
studied and widely used for the description of nuclear systems. However, no
analytical expression for the degeneracy of the 's IR,
determined by the reduction , is available. Thus, the
number of distinct values taken by has been so far obtained by
solving some complex equations. Here we derive analytical expressions for the
degeneracy characterizing the octupole and quadrupole boson states,
respectively. The merit of this work consists of the fact that it completes the
analytical expressions for the -pole boson basis.Comment: 10page
Classical predictability and coarse-grained evolution of the quantum baker's map
We investigate how classical predictability of the coarse-grained evolution
of the quantum baker's map depends on the character of the coarse-graining. Our
analysis extends earlier work by Brun and Hartle [Phys. Rev. D 60, 123503
(1999)] to the case of a chaotic map. To quantify predictability, we compare
the rate of entropy increase for a family of coarse-grainings in the decoherent
histories formalism. We find that the rate of entropy increase is dominated by
the number of scales characterising the coarse-graining.Comment: 28 pages, 1 figur
Compactifications of conformal gravity
We study conformal theories of gravity, i.e. those whose action is invariant
under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is
well known, in order to obtain Einstein gravity in 4D it is necessary to
introduce a scalar compensator with a VEV that spontaneously breaks the
conformal invariance and generates the Planck mass. We show that the
compactification of extra dimensions in a higher dimensional conformal theory
of gravity also yields Einstein gravity in lower dimensions, without the need
to introduce the scalar compensator. It is the field associated with the size
of the extra dimensions (the radion) who takes the role of the scalar
compensator in 4D. The radion has in this case no physical excitations since
they are gauged away in the Einstein frame for the metric. In these models the
stabilization of the size of the extra dimensions is therefore automatic.Comment: 13 page
Weylâs gauge argument
The standard U(1) âgauge principleâ or âgauge argumentâ produces an exact potential A=dλ and a vanishing field F=ddλ=0. Weyl has his own gauge argument, which is sketchy, archaic and hard to follow; but at least it produces an inexact potential A and a nonvanishing field F=dAâ 0. I attempt a reconstruction
Local Conformal Symmetry in Physics and Cosmology
We show how to lift a generic non-scale-invariant action in Einstein frame into a locally conformally invariant (or Weyl-invariant) theory and present a new general form for Lagrangians consistent with Weyl symmetry. Advantages of such a conformally invariant formulation of particle physics and gravity include the possibility of constructing geodesically complete cosmologies. We present a conformal-invariant version of the standard model coupled to gravity, and show how Weyl symmetry may be used to obtain unprecedented analytic control over its cosmological solutions. Within this new framework, generic Friedmann-Robertson-Walker cosmologies are geodesically complete through a series of big crunch-big bang transitions. We discuss a new scenario of cosmic evolution driven by the Higgs field in a âminimalâ conformal standard model, in which there is no new physics beyond the standard model at low energies, and the current Higgs vacuum is metastable as indicated by the latest LHC data
Inflation with a Weyl term, or ghosts at work
In order to assess the role of ghosts in cosmology, we study the evolution of
linear cosmological perturbations during inflation when a Weyl term is added to
the action. Our main result is that vector perturbations can no longer be
ignored and that scalar modes diverge in the newtonian gauge but remain bounded
in the comoving slicing.Comment: 14 pages, 4 figure
Matrix Gravity and Massive Colored Gravitons
We formulate a theory of gravity with a matrix-valued complex vierbein based
on the SL(2N,C)xSL(2N,C) gauge symmetry. The theory is metric independent, and
before symmetry breaking all fields are massless. The symmetry is broken
spontaneously and all gravitons corresponding to the broken generators acquire
masses. If the symmetry is broken to SL(2,C) then the spectrum would correspond
to one massless graviton coupled to massive gravitons. A novel
feature is the way the fields corresponding to non-compact generators acquire
kinetic energies with correct signs. Equally surprising is the way Yang-Mills
gauge fields acquire their correct kinetic energies through the coupling to the
non-dynamical antisymmetric components of the vierbeins.Comment: One reference adde
Topology of the three-qubit space of entanglement types
The three-qubit space of entanglement types is the orbit space of the local
unitary action on the space of three-qubit pure states, and hence describes the
types of entanglement that a system of three qubits can achieve. We show that
this orbit space is homeomorphic to a certain subspace of R^6, which we
describe completely. We give a topologically based classification of
three-qubit entanglement types, and we argue that the nontrivial topology of
the three-qubit space of entanglement types forbids the existence of standard
states with the convenient properties of two-qubit standard states.Comment: 9 pages, 3 figures, v2 adds a referenc
Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
We study the influence of different edge types on the electronic density of
states of graphene nanostructures. To this end we develop an exact expansion
for the single particle Green's function of ballistic graphene structures in
terms of multiple reflections from the system boundary, that allows for a
natural treatment of edge effects. We first apply this formalism to calculate
the average density of states of graphene billiards. While the leading term in
the corresponding Weyl expansion is proportional to the billiard area, we find
that the contribution that usually scales with the total length of the system
boundary differs significantly from what one finds in semiconductor-based,
Schr\"odinger type billiards: The latter term vanishes for armchair and
infinite mass edges and is proportional to the zigzag edge length, highlighting
the prominent role of zigzag edges in graphene. We then compute analytical
expressions for the density of states oscillations and energy levels within a
trajectory based semiclassical approach. We derive a Dirac version of
Gutzwiller's trace formula for classically chaotic graphene billiards and
further obtain semiclassical trace formulae for the density of states
oscillations in regular graphene cavities. We find that edge dependent
interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.
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