10 research outputs found
Self-consistency in Theories with a Minimal Length
The aim of this paper is to clarify the relation between three different
approaches of theories with a minimal length scale: A modification of the
Lorentz-group in the 'Deformed Special Relativity', theories with a
'Generalized Uncertainty Principle' and those with 'Modified Dispersion
Relations'. It is shown that the first two are equivalent, how they can be
translated into each other, and how the third can be obtained from them. An
adequate theory with a minimal length scale requires all three features to be
present.Comment: typos corrected, published with new title following referee's advic
UV divergence-free QFT on noncommutative plane
We formulate Noncommutative Qauntum Field Theory in terms of fields defined
as mean value over coherent states of the noncommutative plane. No *-product is
needed in this formulation and noncommutativity is carried by a modified
Fourier transform of fields. As a result the theory is UV finite and the cutoff
is provided by the noncommutative parameter theta.Comment: 6 pages, Latex, no figures. Accepted for publication in J.Phys.A. New
references adde
Minimal Scales from an Extended Hilbert Space
We consider an extension of the conventional quantum Heisenberg algebra,
assuming that coordinates as well as momenta fulfil nontrivial commutation
relations. As a consequence, a minimal length and a minimal mass scale are
implemented. Our commutators do not depend on positions and momenta and we
provide an extension of the coordinate coherent state approach to
Noncommutative Geometry. We explore, as toy model, the corresponding quantum
field theory in a (2+1)-dimensional spacetime. Then we investigate the more
realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative
planes. As a result, we obtain propagators, which are finite in the ultraviolet
as well as the infrared regime.Comment: 16 pages, version which matches that published on CQ
TeV Mini Black Hole Decay at Future Colliders
It is generally believed that mini black holes decay by emitting elementary
particles with a black body energy spectrum. The original calculation lead to
the conclusion that about the 90% of the black hole mass is radiated away in
the form of photons, neutrinos and light leptons, mainly electrons and muons.
With the advent of String Theory, such a scenario must be updated by including
new effects coming from the stringy nature of particles and interactions.By
taking for granted that black holes can be produced in hadronic collisions,
then their decay must take into account that: (i) we live in a D3-Brane
embedded into an higher dimensional bulk spacetime; (ii) fundamental
interactions, including gravity, are unified at TeV energy scale. Thus, the
formal description of the Hawking radiation mechanism has to be extended to the
case of more than four spacetime dimensions and include the presence of
D-branes. Furthermore, unification of fundamental interactions at an energy
scale many order of magnitude lower than the Planck energy implies that any
kind of fundamental particle, not only leptons, is expected to be emitted. A
detailed understanding of the new scenario is instrumental for optimal tuning
of detectors at future colliders, where, hopefully, this exciting new physics
will be tested. In this article we review higher dimensional black hole decay,
considering not only the emission of particles according to Hawking mechanism,
but also their near horizon QED/QCD interactions. The ultimate motivation is to
build up a phenomenologically reliable scenario, allowing a clear experimental
signature of the event.Comment: 22 pages, 9 figures, 4 tables; ``quick review'' for Class. and
Quantum Gra
The Hawking-Page crossover in noncommutative anti-deSitter space
We study the problem of a Schwarzschild-anti-deSitter black hole in a
noncommutative geometry framework, thought to be an effective description of
quantum-gravitational spacetime. As a first step we derive the noncommutative
geometry inspired Schwarzschild-anti-deSitter solution. After studying the
horizon structure, we find that the curvature singularity is smeared out by the
noncommutative fluctuations. On the thermodynamics side, we show that the black
hole temperature, instead of a divergent behavior at small scales, admits a
maximum value. This fact implies an extension of the Hawking-Page transition
into a van der Waals-like phase diagram, with a critical point at a critical
cosmological constant size in Plank units and a smooth crossover thereafter. We
speculate that, in the gauge-string dictionary, this corresponds to the
confinement "critical point" in number of colors at finite number of flavors, a
highly non-trivial parameter that can be determined through lattice
simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE
Abelian gerbes as a gauge theory of quantum mechanics on phase space
We construct a U(1) gerbe with a connection over a finite-dimensional,
classical phase space P. The connection is given by a triple of forms A,B,H: a
potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength
3-form H=dB. All three of them are defined exclusively in terms of elements
already present in P, the only external input being Planck's constant h. U(1)
gauge transformations acting on the triple A,B,H are also defined, parametrised
either by a 0-form or by a 1-form. While H remains gauge invariant in all
cases, quantumness vs. classicality appears as a choice of 0-form gauge for the
1-form A. The fact that [H]/2i\pi is an integral class in de Rham cohomology is
related with the discretisation of symplectic area on P. This is an equivalent,
coordinate-free reexpression of Heisenberg's uncertainty principle. A choice of
1-form gauge for the 2-form B relates our construction with generalised complex
structures on classical phase space. Altogether this allows one to interpret
the quantum mechanics corresponding to P as an Abelian gauge theory.Comment: 18 pages, 1 figure available from the authors upon reques
Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas
Recently, a new perspective of gravitational-thermodynamic duality as an
entropic force arising from alterations in the information connected to the
positions of material bodies is found. In this paper, we generalize some
aspects of this model in the presence of noncommutative Schwarzschild black
hole by applying the method of coordinate coherent states describing smeared
structures. We implement two different distributions: (a) Gaussian and (b)
Lorentzian. Both mass distributions prepare the similar quantitative aspects
for the entropic force. Our study shows, the entropic force on the smallest
fundamental unit of a holographic screen with radius vanishes. As a
result, black hole remnants are unconditionally inert even gravitational
interactions do not exist therein. So, a distinction between gravitational and
inertial mass in the size of black hole remnant is observed, i.e. the failure
of the principle of equivalence. In addition, if one considers the screen
radius to be less than the radius of the smallest holographic surface at the
Planckian regime, then one encounters some unusual dynamical features leading
to gravitational repulsive force and negative energy. On the other hand, the
significant distinction between the two distributions is conceived to occur
around , and that is worth of mentioning: at this regime either our
analysis is not the proper one, or non-extensive statistics should be employed.Comment: 15 pages, 2 figures, new references added, minor revision, Title
changed, to appear in EPJ Plu