We extend the idea of the generalized Pauli-Villars regularization of Frolov and Slavnov and analyze the general structure of the regularization scheme. The gauge anomaly-free condition emerges in a simple way in the scheme, and, under the standard prescription for the momentum assignment, the Pauli-Villars Lagrangian provides a gauge invariant regularization of chiral fermions in arbitrary ano...

We show that any covariant scattering amplitude of the W 3 string will contain, as part of its integrand, a factor that obeys the differential equations satisfied by an Ising model correlation function. This factor can thus be identified with such a correlation function, in agreement with a previous result of the authors. The W 3 string is also shown to contain an N = 2 parafermion theory, and ...

For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of space-time transformations. These conditions naturally introduce a representation of the group in the space of states. We construct such hyperbolic system from...

We compare the Pegg-Barnett (PB) formalism with the covariant phase observable approach to the problem of quantum phase and show that PB-formalism gives essentially the same results as the canonical (covariant) phase observable. We also show that PB-formalism can be extended to cover all covariant phase observables including the covariant phase observable arising from the angle margin of the Hu...

Using the recently introduced recursion relations with covariant massive-massless shift, we study tree-level scattering amplitudes involving a pair of massive vector bosons and an arbitrary number gluons in spinor-helicity formalism. In particular, derive compact expressions for cases which i) all are same helicity ii) one gluon has flipped is colour adjacent to particles. We provide numerous c...

Solving the so-called geodesic endpoint problem, i.e., finding a that connects two given points on manifold, is at basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On Stiefel manifold orthonormal frames, this problem computationally involved. A remedy to use quasi-geodesics as replacement for Riemannian geodesics. Quasi-geodesic...

Covariant integral quantizations are based on the resolution of identity by continuous or discrete families normalised positive operator valued measures (POVM), which have appealing probabilistic content and transform in a covariant way. One their advantages is to allow circumvent problems due presence singularities classical models. In this paper we implement for systems whose phase space $\ma...

We consider a free photon field in $D$-dimensional de Sitter space, and construct its propagator the general covariant gauge. Canonical quantization is employed to define system starting from classical theory. This guarantees that satisfies both equation of motion subsidiary conditions descending gauge invariance fixing. first as sum-over-modes momentum carefully accounting for symmetry propert...

Abstract The Dowker complex is an abstract simplicial that constructed from a binary relation in straightforward way. Although there are two ways to perform this construction—vertices for the either rows or columns of matrix representing relation—the constructions homotopy equivalent. This article shows construction non-faithful covariant functor. Furthermore, we show functor can be made faithf...