Remarks on Two Approaches to the Horizontal Cohomology: Compatibility Complex and the Koszul-tate Resolution

Remarks on Two Approaches to Thehorizontal Cohomology : Compatibilitycomplex and the Koszul - Tate Resolutionalexander

Notes on the Horizontal Cohomology

This paper is devoted to the horizontal (“characteristic”) cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov C-spectral sequence and Krasilshchik’s C-cohomology are obtained. As an application of general theory, the examples of an evolution equation and a p-form gaug...

Koszul-Tate Cohomology as Lowest-Energy Modules of Non-Centrally Extended Diffeomorphism Algebras

Fock modules for multi-dimensional Virasoro algebras (non-central extensions of the diffeomorphism algebra vect(N)) have recently been reported. Using ideas from the antifield formalism, I construct new classes of lowest-energy modules, as cohomology groups of a certain Fock complex. The Fock construction involves a passage to p-jets prior to normal ordering, but the abelian charges usually div...

A resolution comparison of horizontal and vertical magnetic transfer functions

The main goal of the present study is to identify characteristics of the inter-station horizontal magnetic responses and the vertical magnetic data, as two types of magnetotelluric transfer functions, in the modeling procedure. Through consideration of model responses and two-dimensional inversion of synthetic data, sensitivity of the data components in detecting different geophysical structure...

Quantum physics as the projective representation theory of Noether symmetries

I construct lowest-energy representations of non-centrally extended algebras of Noether symmetries, including diffeomorphisms and reparametrizations of the observer’s trajectory. This may be viewed as a new scheme for quantization. First classical physics is formulated as the cohomology of a certain Koszul-Tate (KT) complex, using not only fields and antifields but also their conjugate momenta....