Narrow Results

We perform the consistent quantization of open string D-brane in non-constant NS–NS closed string B field background by directly imposing the worldsheet conformal symmetry. In addition to the previous noncommutative D-brane coordinates quantization with constant noncommutative parameter θ, we obtain a set of constraints on the B field which can be interpreted as a quantum consistent deformation of a curved noncommutative D-brane.

As a simple example of the "blurring" influence of noncommutative geometry, a noncommutative version of a high-frequency perturbation of a background metric is calculated. The relation between the principal null vectors of the wave and those of the induced symplectic structure is in this case particularly clear.

We study quantum mechanics on the noncommutative cylinder via Moyal deformed geodesic flows on the group of area preserving diffeomorphism. This equation coincides exactly with the von Neumann equation. Using discretization techniques of Kemmoku and Saito we obtain the discrete Schrödinger equation on noncommutative cylinder. Thus we reproduce the result of Balachandran et al.¹

Using the generalized graded differential algebra of Doebner–Tahiri and the left covariant differential calculus on su_q(2) of Woronowicz, we could determine explicitly the quantum fields and their quantum BRST transformations. We have also derived the covariant derivative of the matter fields and the q-Bianchi identities.

In this paper, we have constructed the Green function of the Feshbach–Villars (FV) spinless particle in a noncommutative (NC) phase-space coordinates, where the Pauli matrices describing the charge symmetry are replaced by the Grassmannian odd variables. Subsequently, for the perform calculations, we diagonalize the Hamiltonian governing the dynamics of the system via the Foldy–Wouthuysen (FW) canonical transformation. The exact calculations have been done in the cases of free particle and magnetic field interaction. In both cases, the energy eigenvalues and their corresponding eigenfunctions are deduced.

In this talk we present a field theoretical model constructed in Minkowski superspace with a deformed supercoordinate algebra. Our study is motivated in part by recent results from super-string theory, which show that in a particular scenario in Euclidean superspace the spinor coordinates θ do not anticommute. Field theoretical consequences of this deformation were studied in a number of articles. We present a way to extend the discussion to Minkowski space, by assuming non-vanishing anticommutators for both θ, and . We give a consistent supercoordinate algebra, and a star product that is real and preserves the (anti)chirality of a product of (anti)chiral superfields. We also give the Wess-Zumino Lagrangian that gains only Lorentz-invariant corrections due to non(anti)commutativity within our model. The Lagrangian in Minkowski superspace is also always manifestly Hermitian.

We present a new procedure for quantizing field theory models on a noncommutative space–time. Our new quantization scheme depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by this quantization yields exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after the quantization. This implies, for instance, that the noncommutativity may be incorporated in the process of quantization, rather than in the action as conventionally done.

The Hamiltonian of two modes coupled harmonic oscillators in noncommutative phase-space can be expressed in the standard quadric form by introducing a coordinate transformation. As a result, the coupling items are eliminated and the Hamiltonian can be simplified to the two modes independent harmonic oscillators. Then, the corresponding energy spectrums are obtained with an algebraic method.

Chern–Simons mechanics in noncommutative phase space is studied from both classical and quantum aspects in this paper. We find that there are two parameters in the full theory which lead to two different reduced theories when they take certain values. We analyze these two reduced models also from two aspects and find that the classical aspect of the full theory has a continuous limit when both of these parameters take their certain values. However, the quantum aspect of the full theory does not have the similar limit. The spectra of the full theory will be infinite when these parameters take these values. We propose artificial regularization schemes to get rid of these infinity and resort to Dirac's theories to verify our scheme.

The finite embeddability property (FEP) for knotted extensions of residuated lattices holds under the assumption of commutativity, but fails in the general case. We identify weaker forms of the commutativity identity which ensure that the FEP holds. The results have applications outside of order algebra to non-classical logic, establishing the strong finite model property (SFMP) and the decidability for deductions, as well as to mathematical linguistics and automata theory, providing new conditions for recognizability of languages. Our proofs make use of residuated frames, developed in the context of algebraic proof theory.

A revision of generalized commutation relations is performed, besides a description of nonlinear momenta realization included in some DSR theories. It is shown that these propositions are closely related, specially we focus on Magueijo–Smolin momenta and Kempf et al. and Chang generalized commutators. Due to this, a new algebra arises with its own features that is also analyzed.

We revisit the issue of continuous signature transition from Euclidean to Lorentzian metrics in a cosmological model described by Friedmann–Robertson–Walker (FRW) metric minimally coupled with a self-interacting massive scalar field. Then, using a noncommutative (NC) phase space of dynamical variables deformed by generalized uncertainty principle (GUP), we show that the signature transition occurs even for a model described by the FRW metric minimally coupled with a free massless scalar field accompanied by a cosmological constant. This indicates that the continuous signature transition might have been easily occurred at early universe just by a free massless scalar field, a cosmological constant and a NC phase space deformed by GUP, without resorting to a massive scalar field having an ad hoc complicate potential. We also study the quantum cosmology of the model and obtain a solution of Wheeler–DeWitt (WD) equation which shows a good correspondence with the classical path.

In this paper, we show how it is possible to obtain mass generation in the context of non-Abelian gauge field theory, using a noncommutative spacetime. This is further confirmed by the modified dispersion relation that results from such a geometry. Other effects in the domain of ultra high energy gamma rays and cosmic rays are also deduced and it is pointed out that we might already have observed such effects.

It is argued that electric and magnetic fields are generated by the noncommutative geometry at high energies rather like the minimum conductivity in graphene. An exact Reynolds number type of correspondence between graphene and high energy phenomena is also established.

As a historical remark the similarities are pointed out between a form of chiral action introduced by Schwinger and the formalism used in the noncommutative extensions of electromagnetism.

In this paper we propose a new concept of prime ideals in noncommutative quantales. The usual definition of prime ideal is preserved as a completely prime ideal. In this investigation it is proved that these two concepts coincide in commutative quantales, but are no longer valid in the noncommutative setting.