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.

Creeping flow past rotating axi-symmetric isolated body-class of deformed sphere

In a recent paper, Srivastava et al. (Int J Appl Math Mech 8:17–53, 2012) tackled the problem of steady Stokes flow around deformed sphere wherein author evaluated the general expression of drag with the help of method developed by Datta and Srivastava (Proc Indian Acad Sci Math Sci 109:441–452, 1999) in both situations when axially symmetric isolated body is placed under axial flow (along the axis of symmetry) and transverse flow(along perpendicular to axis of symmetry) corrected up to the second order of deformation parameter and applied those on to class of oblate bodies and to flat circular disk as a special case. In this paper, rotation of deformed sphere has been dealt in axial or longitudinal situation in which uniform stream is along the axis of symmetry under the no-slip boundary conditions. The general expression of torque in terms of axial Stokes drag (Srivastava et al., Int J Appl Math Mech 8:17–53, 2012) is produced with the help of method developed by Datta and Srivastava (Proc Indian Acad Sci Math Sci 109:441–452, 1999). The general form of deformed sphere, governed by polar equation, $$r = a(1 + \varepsilon \sum\nolimits_{k = 0}^{\infty } {d_{k} P_{k} ({ \cos } \theta )} )$$ (where, d k is shape factor and P k is Legendre function of first kind), is considered for the study. The expression of torque for slowly rotating deformed sphere is derived up to the order of O(e 2). The class of oblate and prolate axisymmetric bodies is considered for the validation and further numerical discussion. All the expressions of moment coefficients are updated up to the order of O(e 2), where e is deformation parameter. In particular, up to the order of O(e) and O(e 2), the numerical values of moment coefficients and their ratio have been evaluated for the various values of deformation parameters(e) and aspect ratio(b/a) for a class of oblate and prolate axially symmetric bodies including disk and thin slender elongated bodies as a special cases.

Different realizations ofκ-momentum space

We consider different realizations for the momentum sector of kappa-Poincare Hopf algebra, which is associated with a curved momentum space. We show that the notion of the particle mass as introduced recently by Amelino-Camelia et al. in the context of relative-locality is realization independent for a wide class of realizations, up to linear order in deformation parameter l. On the other hand, the time delay formula clearly shows a dependence on the choice of realization.

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.

Kappa Snyder deformations of Minkowski spacetime, realizations, and Hopf algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are however isomorphic at the level of Hopf algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. Deformed Leibniz rule, the Hopf structure and star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations are discussed. The same generalized Hopf algebraic structures are as well considered in the case of an arbitrary allowable kind of realisation and results are given perturbatively up to second order in deformation parameters.

Instanton calculus in R-R 3-form background and deformed 𝒩 = 2 super Yang-Mills theory

We study the ADHM construction of instantons in = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(−1) branes at the orbifold singularity of C2/Z2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(−1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the Ω-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.

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.