相关论文: Higher order reduction theorems for general linear…
It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce…
The geometry of the total space of a principal bundle with regard to the action of the bundle's structure group is elegantly described by the bundle's operation, a collection of derivations consisting of the de Rham differential and the…
For a real or complex semisimple Lie group $G$ and two nested parabolic subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$. Associated to the group $P$, we introduce a class of relative natural bundles and…
Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic…
The reductions of an ideal $I$ give a natural pathway to the properties of $I$, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of…
To solve the quantum-mechanical problem the procedure of mapping onto linear space $W$ of generators of the (sub)group violated by given classical trajectory is formulated. The formalism is illustrated by the plane H-atom model. The problem…
In effective quantum field theories, higher dimensional operators can affect the canonical normalization of kinetic terms at tree level. These contributions for scalars and gauge bosons should be carefully included in the gauge fixing…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…
The semiclassical backreaction equations are solved in closed Robertson-Walker spacetimes containing a positive cosmological constant and a conformally coupled massive scalar field. Renormalization of the stress-energy tensor results in…
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…
We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…
In the main part of this paper a connection is just a fiber projection onto a (not necessarily integrable) distribution or sub vector bundle of the tangent bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it is…
Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was…
We formulate and establish a generalization of Koll\'ar's injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Koll\'ar's torsion-freeness, Koll\'ar's vanishing theorem, and a…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…