Related papers: Lectures on the fourth order Q curvature equation
The geometry of the rotating disk is revisited and the quantum consequences are discussed. A suggestion to detect the presence of the Gaussian curvature on the rotating disk only measuring transition frequencies is made. A quantum…
Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in…
These lectures deal with selected aspects of quantum field theory in curved spacetime including the following topics: (1) Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an…
Mean curvature flows of hypersurfaces have been extensively studied and there are various different approaches and many beautiful results. However, relatively little is known about mean curvature flows of submanifolds of higher…
We describe a q-deformation of the Lorentz group in terms of a q-deformation of the van der Waerden spinor algebra.
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
This is a survey paper. We discuss Toeplitz operators in K\"ahler geometry, with applications to geometric quantization, and review some recent developments.
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
The relations between the second order ODE's cubical on the first derivative and their dual equations are discussed
We discuss QCD studies that will be possible at LEP2. We examine both experimental and theoretical aspects of jets, fragmentation functions, multiplicities and particle spectra.
A nonstandard invariant fourth order operator acting on functions on a manifold equipped with an almost Grassmannian structure with an arbitrary trorsion is found by means of the curved translation principle. This operator can be viewed as…
We calculate higher-order quantum contributions in different Lorentz-violating parameters to the gauge sector of the extended QED. As a result of this one-loop calculation, some terms which do not produce first-order corrections, contribute…
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski-space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore,…
In a recent paper [J.Math.Phys. vol42, 2236-2265 (2001)], we discussed differential operators within a quaternionic formulation of quantum mechanics. In particular, we proposed a practical method to solve quaternionic and complex linear…
We make several improvements on the results of M.-T. Wang in [8] and his joint paper with M.-P. Tsui [7] concerning the long time existence and convergence for solutions of mean curvature flow in higher co-dimension. Both the curvature…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
In this proceedings for the MG14 conference, we discuss the construction of a phenomenology of Planck-scale effects in curved spacetimes, underline a few open issues and describe some perspectives for the future of this research line.
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
We establish linear profile decompositions for the fourth order Schr\"odinger equation and for certain fourth order perturbations of the Schr\"odinger equation, in dimensions greater than or equal to two. We apply these results to prove…