1,890 research outputs found
Discreteness of Space from the Generalized Uncertainty Principle
Various approaches to Quantum Gravity (such as String Theory and Doubly
Special Relativity), as well as black hole physics predict a minimum measurable
length, or a maximum observable momentum, and related modifications of the
Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty
Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special
Relativity and black hole physics, and show that this modifies all quantum
mechanical Hamiltonians. When applied to an elementary particle, it implies
that the space which confines it must be quantized. This suggests that space
itself is discrete, and that all measurable lengths are quantized in units of a
fundamental length (which can be the Planck length). On the one hand, this
signals the breakdown of the spacetime continuum picture near that scale, and
on the other hand, it can predict an upper bound on the quantum gravity
parameter in the GUP, from current observations. Furthermore, such fundamental
discreteness of space may have observable consequences at length scales much
larger than the Planck scale.Comment: 3 pages, revtex4, no figures, to appear in Phys. Lett.
Symmetry breaking aspects of the effective Lagrangian for quantum black holes
The physical excitations entering the effective Lagrangian for quantum black
holes are related to a Goldstone boson which is present in the Rindler limit
and is due to the spontaneous breaking of the translation symmetry of the
underlying Minkowski space. This physical interpretation, which closely
parallels similar well-known results for the effective stringlike description
of flux tubes in QCD, gives a physical insight into the problem of describing
the quantum degrees of freedom of black holes. It also suggests that the
recently suggested concept of 'black hole complementarity' emerges at the
effective Lagrangian level rather than at the fundamental level.Comment: 11 pages, Latex,1 figur
Discreteness of Space from GUP II: Relativistic Wave Equations
Various theories of Quantum Gravity predict modifications of the Heisenberg
Uncertainty Principle near the Planck scale to a so-called Generalized
Uncertainty Principle (GUP). In some recent papers, we showed that the GUP
gives rise to corrections to the Schrodinger equation, which in turn affect all
quantum mechanical Hamiltonians. In particular, by applying it to a particle in
a one dimensional box, we showed that the box length must be quantized in terms
of a fundamental length (which could be the Planck length), which we
interpreted as a signal of fundamental discreteness of space itself. In this
paper, we extend the above results to a relativistic particle in a rectangular
as well as a spherical box, by solving the GUP-corrected Klein-Gordon and Dirac
equations, and for the latter, to two and three dimensions. We again arrive at
quantization of box length, area and volume and an indication of the
fundamentally grainy nature of space. We discuss possible implications.Comment: v1:8 pages, revtex4, no figures, to appear in Phys. Lett. B; v2:
version to match published version in PLB, corrections in ERRATUM include
Extracting the three- and four-graviton vertices from binary pulsars and coalescing binaries
Using a formulation of the post-Newtonian expansion in terms of Feynman
graphs, we discuss how various tests of General Relativity (GR) can be
translated into measurement of the three- and four-graviton vertices. In
problems involving only the conservative dynamics of a system, a deviation of
the three-graviton vertex from the GR prediction is equivalent, to lowest
order, to the introduction of the parameter beta_{PPN} in the parametrized
post-Newtonian formalism, and its strongest bound comes from lunar laser
ranging, which measures it at the 0.02% level. Deviation of the three-graviton
vertex from the GR prediction, however, also affects the radiative sector of
the theory. We show that the timing of the Hulse-Taylor binary pulsar provides
a bound on the deviation of the three-graviton vertex from the GR prediction at
the 0.1% level. For coalescing binaries at interferometers we find that,
because of degeneracies with other parameters in the template such as mass and
spin, the effects of modified three- and four-graviton vertices is just to
induce an error in the determination of these parameters and, at least in the
restricted PN approximation, it is not possible to use coalescing binaries for
constraining deviations of the vertices from the GR prediction.Comment: 10 pages, 5 figures; v2: an error corrected; references adde
A Multi Megawatt Cyclotron Complex to Search for CP Violation in the Neutrino Sector
A Multi Megawatt Cyclotron complex able to accelerate H2+ to 800 MeV/amu is
under study. It consists of an injector cyclotron able to accelerate the
injected beam up to 50 MeV/n and of a booster ring made of 8 magnetic sectors
and 8 RF cavities. The magnetic field and the forces on the superconducting
coils are evaluated using the 3-D code OPERA. The injection and extraction
trajectories are evaluated using the well tested codes developed by the MSU
group in the '80s. The advantages to accelerate H2+ are described and
preliminary evaluations on the feasibility and expected problems to build the
injector cyclotron and the ring booster are here presented.Comment: Presentation at Cyclotron'10 conference, Lanzhou, China, Sept 7, 201
Algebraic renormalization of supersymmetric gauge theories with dimensionful parameters
It is usually believed that there are no perturbative anomalies in
supersymmetric gauge theories beyond the well-known chiral anomaly. In this
paper we revisit this issue, because previously given arguments are incomplete.
Specifically, we rule out the existence of soft anomalies, i.e., quantum
violations of supersymmetric Ward identities proportional to a mass parameter
in a classically supersymmetric theory. We do this by combining a previously
proven theorem on the absence of hard anomalies with a spurion analysis, using
the methods of Algebraic Renormalization. We work in the on-shell component
formalism throughout. In order to deal with the nonlinearity of on-shell
supersymmetry transformations, we take the spurions to be dynamical, and show
how they nevertheless can be decoupled.Comment: Final version, typoes fixed. Revtex, 48 page
Wave Packets Propagation in Quantum Gravity
Wave packet broadening in usual quantum mechanics is a consequence of
dispersion behavior of the medium which the wave propagates in it. In this
paper, we consider the problem of wave packet broadening in the framework of
Generalized Uncertainty Principle(GUP) of quantum gravity. New dispersion
relations are derived in the context of GUP and it has been shown that there
exists a gravitational induced dispersion which leads to more broadening of the
wave packets. As a result of these dispersion relations, a generalized
Klein-Gordon equation is obtained and its interpretation is given.Comment: 9 pages, no figur
Spectrum of relic gravitational waves in string cosmology
We compute the spectrum of relic gravitons in a model of string cosmology. In the low- and in the high-frequency limits we reproduce known results. The full spectrum, however, also displays a series of oscillations which could give a characteristic signature at the planned LIGO/VIRGO detectors. For special values of the parameters of the model the signal reaches its maximum already at frequencies accessible to LIGO and VIRGO and it is close to the sensitivity of first generation experiments
Sensitivity of spherical gravitational-wave detectors to a stochastic background of non-relativistic scalar radiation
We analyze the signal-to-noise ratio for a relic background of scalar
gravitational radiation composed of massive, non-relativistic particles,
interacting with the monopole mode of two resonant spherical detectors. We find
that the possible signal is enhanced with respect to the differential mode of
the interferometric detectors. This enhancement is due to: {\rm (a)} the
absence of the signal suppression, for non-relativistic scalars, with respect
to a background of massless particles, and {\rm (b)} for flat enough spectra, a
growth of the signal with the observation time faster than for a massless
stochastic background.Comment: four pages, late
An Improved Calculation of the Non-Gaussian Halo Mass Function
The abundance of collapsed objects in the universe, or halo mass function, is
an important theoretical tool in studying the effects of primordially generated
non-Gaussianities on the large scale structure. The non-Gaussian mass function
has been calculated by several authors in different ways, typically by
exploiting the smallness of certain parameters which naturally appear in the
calculation, to set up a perturbative expansion. We improve upon the existing
results for the mass function by combining path integral methods and saddle
point techniques (which have been separately applied in previous approaches).
Additionally, we carefully account for the various scale dependent combinations
of small parameters which appear. Some of these combinations in fact become of
order unity for large mass scales and at high redshifts, and must therefore be
treated non-perturbatively. Our approach allows us to do this, and to also
account for multi-scale density correlations which appear in the calculation.
We thus derive an accurate expression for the mass function which is based on
approximations that are valid over a larger range of mass scales and redshifts
than those of other authors. By tracking the terms ignored in the analysis, we
estimate theoretical errors for our result and also for the results of others.
We also discuss the complications introduced by the choice of smoothing filter
function, which we take to be a top-hat in real space, and which leads to the
dominant errors in our expression. Finally, we present a detailed comparison
between the various expressions for the mass functions, exploring the accuracy
and range of validity of each.Comment: 28 pages, 13 figures; v2: text reorganized and some figured modified
for clarity, results unchanged, references added. Matches version published
in JCA
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