相关论文: Twisted Dirac Operators over Quantum Spheres
The torus group $(S^1)^{\ell+1}$ has a canonical action on the odd dimensional sphere $S_q^{2\ell+1}$. We take the natural Hilbert space representation where this action is implemented and characterize all odd spectral triples acting on…
In this paper, we present an explicit construction of twisted traces for quantum Coulomb branches of conical theories. We develop an operator representation of the Coulomb branch algebra and use it to derive integral formulas for the…
We give a survey on the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional and on related problems of spectral theory of the two-dimensional Dirac…
Transversely polarized Lambda production in hard scattering processes is discussed in terms of a leading twist T-odd fragmentation function which describes the fragmentation of an unpolarized quark into a transversely polarized Lambda. We…
In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…
We find and classify possible equivariant spin structures with Dirac operators on the noncommutative torus, proving that similarly as in the classical case the spectrum of the Dirac operator depends on the spin structure.
We discuss twisted cohomology, not just for ordinary cohomology but also for $K$-theory and other exceptional cohomology theories, and discuss several of the applications of these in mathematical physics. Our list of applications is by no…
The Weierstrass representation for spheres in $\R^3$ and, in particular, effective construction of immersions from data of spectral theory origin is discussed. These data are related to Dirac operators on a plane and on an infinite cylinder…
A new package, DISPred, is described. The package can be used to calculate ep deep inelastic scattering cross sections at Born level in Electroweak theory and at both leading and next-to-leading order in QCD.
Several important observables, like the quark condensate and the Taylor coefficients of the expansion of the QCD pressure with respect to the chemical potential, are based on the trace of the inverse Dirac operator and of its powers. Such…
Given a plane triangle $\Delta$, one can construct a new triangle $\Delta'$ whose vertices are intersections of two cevian triples of $\Delta$. We extend the family of operators $\Delta\mapsto\Delta'$ by complexifying the defining two…
We unravel the structure of the spectrum of the anomalous dimensions of the quark-gluon twist-3 operators which are responsible for the multiparton correlations in hadrons and enter as a leading contribution to several physical cross…
We study the effect of quantum Frobenius twist on Ext-groups in the category of quantum polynomial, and prove that the existence of type of complexes, called quantum Troesch complexes, enables the construction of a spectral sequence…
We construct twisting functors for quantum group modules. First over the field $\mathbb{Q}(v)$ but later over any $\mathbb{Z} [v,v^{-1}]$-algebra. The main results in this paper are a rigerous definition of these functors, a proof that they…
In this paper we explicitly compute equations for the twists of all the smooth plane quartic curves defined over a number field k. Since the plane quartic curves are non-hyperelliptic curves of genus 3 we can apply the method developed by…
We study the Penrose transform for the `quaternionic objects' whose twistor spaces are complex manifolds endowed with locally complete families of embedded Riemann spheres with positive normal bundles.
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…