Related papers: Integration on differential spaces
The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…
We develop a theory of conically smooth stratified spaces and their smooth moduli, including a notion of classifying maps for tangential structures. We characterize continuous space-valued sheaves on these conically smooth stratified spaces…
The paper provides a description of the sheaves of K\"ahler differentials of the arc space and jet schemes of an arbitrary scheme where these sheaves are computed directly from the sheaf of differentials of the given scheme. Several…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…
A new characterization of conformal transformations is given. By use of this, the general form of conformal transformation on two-dimensional Minkowski space is given and its conformal structure is analyzed.
We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…
In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…
We consider a relation between local and global characteristics of a differential algebraic variety. We prove that dimension of tangent space for every regular point of an irreducible differential algebraic variety coincides with dimension…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We discuss the dimensional characterization of the solutions space of a formally integrable system of partial differential equations and provide certain formulas for calculations of these dimensional quantities.
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.