Modern Physics Letters A

Starting from deformed coordinates a covariant deformation of the Poincaré and Heisenberg algebra is derived. The deformation function is determined uniquely by the Jacobi identities leading to noncommutative coordinates, a generalized uncertainty principle and deformed Lorentz transformations.

From the study of well-known divergent amplitudes we deduce three consistency conditions which are necessary and sufficient to eliminate ambiguities and symmetry violations. The conditions relate divergent integrals of the same degree of divergence and are automatically satisfied within the context of dimensional regularization. We show how the deduced consistency conditions can be satisfied in four-dimensional regularizations. An important conclusion of the present study is the possibility of working with 4-D regularization schemes which preserve the virtues of dimensional regularization avoiding, however, its restrictions.

New solution of a classical Yang–Baxter equation on a loop extended, "modified" Lie algebra of a diffeomorphism group of a torus dĩff(T²)[λ]is given.

Lie bialgebra structure on dĩff(T²)[λ] is defined. By quantization of a defined Lie bialgebra, a Yangian algebra Y(dĩff(T²)) is obtained.

Existence of a quantum double and a quantum R-matrix for Y(dĩff(T²)) is considered.

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4SU(2) SYM effective action.

Relativistic quantum field theories predict negative energy densities, contravening a basic tenet of classical physics and a fundamental hypothesis of the deepest results in classical general relativity. These densities may be sources for exotic general relativistic effects, and may also lead to pathologies.

Combining Ford's "quantum inequality" with quantum restrictions on measuring devices, we present an argument that these densities nevertheless satisfy a sort of "operational" positivity: the energy in a region, plus the energy of an isolated device designed to detect or trap the exotic energy, must be non-negative. This will suppress at least some pathological effects.

If we suppose also that Einstein's field equation holds, then no local observer can measure the geometry of a negative energy density regime accurately enough to infer a negative energy density form the curvature. This means that the physics of a negative energy regime cannot be adequately modeled by a classical space–time.

We give a two-parameter quantum deformation of the exterior plane and its differential calculus without the use of any R-matrix and relate it to the differential calculus with the R-matrix. We prove that there are two types of solutions of the Yang–Baxter equation whose symmetry group is GL_p,q(2). We also give a two-parameter deformation of the fermionic oscillator algebra.

In this letter we signalize the possibility of applying a quantum chaos as an element of high sensitivity which serves to detect small changes in length generated by gravitational waves. We propose the construction of a double-bar antenna with a coupling Josephson junction in its center-of-mass. In fact the new antenna is a single Josephson junction with massive bulk contacts, like a single-junction SQUID but with free ends. Computer experiments demonstrate that very small changes generated by the variation of the distance between the bulk plates of the junction capacitance will produce a variety of very different intermittency routes to chaos. A concrete numerical example illustrates the smallness of a quantum of chaos and thus the extraordinary sensitivity of the proposed method.

We study the domain-wall formalism with additional Majorana mass term for the unwanted zero-mode, which has recently been proposed for lattice construction of 4D super-Yang–Mills theory without fine-tuning. Switching off the gauge field, we study the dispersion relation of the energy eigenstates numerically, and find that the method works for reasonable values of Majorana mass. We point out, however, that when the Majorana mass is too large, a problem arises which can be explained in terms of seesaw mechanism.