Unsharp Degrees of Freedom and the Generating of Symmetries

In quantum theory, real degrees of freedom are usually described by operators which are self-adjoint. There are, however, exceptions to the rule. This is because, in infinite dimensional Hilbert spaces, an operator is not necessarily self-adjoint even if its expectation values are real. Instead, the operator may be merely symmetric. Such operators are not diagonalizable - and as a consequence they describe real degrees of freedom which display a form of "unsharpness" or "fuzzyness". For example, there are indications that this type of operators could arise with the description of space-time at the string or at the Planck scale, where some form of unsharpness or fuzzyness has long been conjectured. A priori, however, a potential problem with merely symmetric operators is the fact that, unlike self-adjoint operators, they do not generate unitaries - at least not straightforwardly. Here, we show for a large class of these operators that they do generate unitaries in a well defined way, and that these operators even generate the entire unitary group of the Hilbert space. This shows that merely symmetric operators, in addition to describing unsharp physical entities, may indeed also play a r{\^o}le in the generation of symmetries, e.g. within a fundamental theory of quantum gravity.Comment: 23 pages, LaTe

On Fields with Finite Information Density

The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.Comment: 31 pages, to appear in Phys.Rev.

Lorentz-covariant deformed algebra with minimal length

The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special case. The deformed Poincar\'e transformations leaving the algebra invariant are identified. Uncertainty relations are studied. In the case of D=1 and one nonvanishing parameter, the bound-state energy spectrum and wavefunctions of the Dirac oscillator are exactly obtained.Comment: 8 pages, no figure, presented at XV International Colloquium on Integrable Systems and Quantum Symmetries (ISQS-15), Prague, June 15-17, 200

Quantum Theory of Noncommutative Fields

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given.Comment: LaTeX file, JHEP3.cls, subequations.sty; 12 pages, no figures. Final version published in JHEP with some references adde

Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation

We continue our investigation of the phenomenological implications of the "deformed" commutation relations [x_i,p_j]=i hbar[(1 + beta p^2) delta_{ij} + beta' p_i p_j]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.Comment: 20 pages REVTEX4, 4 color eps figures, typos correcte

Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics

In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.Comment: 21 Pages, 3 eps Figure, Revised Versio

Transdimensional physics and inflation

Within the framework of a five-dimensional brane world with a stabilized radion, we compute the cosmological perturbations generated during inflation and show that the perturbations are a powerful tool to probe the physics of extra dimensions. While we find that the power spectrum of scalar perturbations is unchanged, we show that the existence of the fifth dimension is imprinted on the spectrum of gravitational waves generated during inflation. In particular, we find that the tensor perturbations receive a correction proportional to $(HR)^2$, where $H$ is the Hubble expansion rate during inflation and $R$ is the size of the extra dimension. We also generalize our findings to the case of several extra dimensions as well as to warped geometries.Comment: RevTeX file, 30 pages, 1 figure. Final version to appear in PR

Primeval Corrections to the CMB Anisotropies

We show that deviations of the quantum state of the inflaton from the thermal vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum dynamics of the inflaton in such a state produces corrections to the inflationary fluctuations, which may be observable. Because these effects originate from IR physics below the Planck scale, they will dominate over any trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps away these initial deviations and forces its quantum state closer to the thermal vacuum. We view this as the quantum version of the cosmic no-hair theorem. Such imprints in the CMB may be a useful, independent test of the duration of inflation, or of significant features in the inflaton potential about 60 e-folds before inflation ended, instead of an unlikely discovery of the signatures of quantum gravity. The absence of any such substructure would suggest that inflation lasted uninterrupted much longer than ${\cal O}(100)$ e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final version to appear in Phys. Rev.

Hawking Temperature in Taub-NUT (A)dS spaces via the Generalized Uncertainty Principle

Using the extended forms of the Heisenberg uncertainty principle from string theory and the quantum gravity theory, we drived Hawking temperature of a Taub-Nut-(A)dS black hole. In spite of their distinctive natures such as asymptotically locally flat and breakdown of the area theorem of the horizon for the black holes, we show that the corrections to Hawking temperature by the generalized versions of the the Heisenberg uncertainty principle increases like the Schwarzschild-(A)dS black hole and give the reason why the Taub-Nut-(A)dS metric may have AdS/CFT dual picture.Comment: version published in General Relativity and Gravitatio

Superimposed Oscillations in the WMAP Data?

The possibility that the cosmic variance outliers present in the recently released WMAP multipole moments are due to oscillations in the primordial power spectrum is investigated. Since the most important contribution to the WMAP likelihood originates from the outliers at relatively small angular scale (around the first Doppler peak), special attention is paid to these in contrast with previous studies on the subject which have concentrated on the large scales outliers only (i.e. the quadrupole and octupole). As a physically motivated example, the case where the oscillations are of trans-Planckian origin is considered. It is shown that the presence of the oscillations causes an important drop in the WMAP chi square of about fifteen. The F-test reveals that such a drop has a probability less than 0.06% to occur by chance and can therefore be considered as statistically significant.Comment: 9 pages, 3 figures, uses RevTex 4, references added, matches published versio