First Order In Deformation Parameter Research Articles

Emergence of maximal acceleration from non-commutativity of spacetime

In this paper, we show that the causally connected four-dimensional line element of the [Formula: see text]-deformed Minkowski spacetime induces an upper cut-off on the proper acceleration and derive this maximal acceleration, valid up to first order in the deformation parameter. We find a contribution to maximal acceleration which is independent of [Formula: see text] and thus signals effect of the non-commutativity alone. We also construct the [Formula: see text]-deformed geodesic equation and obtain its [Formula: see text]-deformed Newtonian limit, valid up to first order in deformation parameter. Using this, we constrain non-commutative parameters present in the expression for maximal acceleration. We analyze different limits of the maximal acceleration and also discuss its implication to maximal temperature. We also obtain a bound on the deformation parameter.

Macroscopic detection of deformed QM by the harmonic oscillator

Based on the nonperturbative analysis, we show that the classical motion of harmonic oscillator derived from the deformed QM is manifestly in contradiction with observations (to the first order in deformation parameter as it has been pointed out in Bawaj et al. (2015)). For this reason, we take an alternate way for estimating the effect and discuss its possible observational manifestations in macrophysics.

Extra-dimensional generalization of minimum-length deformed QM/QFT and some of its phenomenological consequences

In contrast to the 3D case, different approaches for deriving the gravitational corrections to the Heisenberg uncertainty relation do not lead to the unique result whereas additional spatial dimensions are present in the theory. We suggest to take logarithmic corrections to the black hole entropy, which has recently been proved both in string theory and loop quantum gravity to persist in presence of additional spatial dimensions, as a point of entry for identifying the modified Heisenberg-Weyl algebra. We then use a particular Hilbert space representation for such a quantum mechanics to construct the correspondingly modified field theory and address some phenomenological issues following from it. Some subtleties arising at the second quantization level are clearly pointed out. Solving the field operator to the first order in deformation parameter and defining the modified wave function for a free particle, we discuss the possible phenomenological implications for the black hole evaporation. Putting aside modifications arising at the second quantization level, we address the corrections to the gravitational potential due to modified propagator (back reaction on gravity) and see that correspondingly modified Schwarzschild-Tangherlini space-time shows up the disappearance of the horizon and vanishing of surface gravity when black hole mass approaches the quantum gravity scale. This result points out to the existence of zero-temperature black hole remnants.

Minimum-length deformed quantization of a free field on the de Sitter background and corrections to the inflaton perturbations

The effect of string and quantum gravity inspired minimum-length deformed quantization on a free, massless scalar field is studied on de Sitter background at the level of second quantization. Analytic solution of a field operator is obtained to the first order in deformation parameter. Using this solution we then estimate the two point and four point correlation functions (with respect to the Bunch-Davies vacuum). The field operator shows up a non-linear dependence on creation and annihilation operators, therefore the perturbation spectrum proves to be non-Gaussian. The correction to the power spectrum is of the same order as obtained previously in a similar study that incorporates the minimum-length deformed momentum operator into the first quantization picture and then proceeds in the standard way for second quantization. The non-Gaussianity comes at the level of four point correlation function; its magnitude appears to be suppressed by the factor $\sim\exp(-6N)$, where $N$ is the number of e-foldings.

Corrections to the black body radiation due to minimum-length deformed quantum mechanics

Planck spectrum of black body radiation is usually derived by considering of quantized free electromagnetic field at a finite temperature. The minimum-length deformed quantization affects field theory both at the first and second quantization levels. Performing an exact calculation to the first order in deformation parameter, both of the corrections turn out to be of the same order. Nevertheless, the correction at the second quantization level has some qualitative difference, that may be interesting for future study to differentiate between these two sorts of corrections. In itself the correction to the black body radiation seems to be innocuous in light of the big-bang nucleosynthesis whenever the minimum length is less or equal to 10−19 cm.

An invariant action for noncommutative gravity in four dimensions

Two main problems face the construction of noncommutative actions for gravity with star products: the complex metric and finding an invariant measure. The only gauge groups that could be used with star products are the unitary groups. I propose an invariant gravitational action in D=4 dimensions based on the constrained gauge group U(2,2) broken to U(1,1)×U(1,1). No metric is used, thus giving a naturally invariant measure. This action is generalized to the noncommutative case by replacing ordinary products with star products. The four-dimensional noncommutative action is studied and the deformed action to first order in deformation parameter is computed.