Related papers: DeWitt-Virasoro construction in tensor representat…
Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…
A model, based on a noncommutative geometry, unifying general relativity with quantum mechanics, is further develped. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators. It is…
We give a computability result for open Gromov-Witten invariants based on open WDVV equations. This is analogous to the result of Kontsevich-Manin for closed Gromov-Witten invariants. For greater generality, we base the argument on a formal…
Scissor lifts, a staple of mechanical design, especially in competitive robotics, are a type of linkage that can be used to raise a load to some height, when acted upon by some force, usually exerted by an actuator. The position of this…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
It is shown that conventional "covariant" derivative of the Levi-Civita tensor is not really covariant. Adding compensative terms, it is possible to make it covariant and to be equal to zero. Then one can be introduced a curvature in the…
On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering…
We consider axial torsion fields which appear in higher derivative quantum gravity. It is shown, in general, that the torsion field possesses states with two spins, one and zero, with different masses. The first-order formulation of torsion…
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…
For an arbitrary commutative ring k and t in k, we construct a 2-functor S_t which sends a tensor category to a new tensor category. By applying it to the representation category of a bialgebra we obtain a family of categories which…
We make a direct connection between the construction of three dimensional topological state sums from tensor categories and three dimensional quantum gravity by noting that the discrete version of the Wheeler-DeWitt equation is exactly the…
We construct gauge theory of interacting symmetric traceless tensor fields of all ranks s=0,1,2,3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d>2. The action is given by the trace of the…
An optimal rank-1 approximation of state transition tensors was developed as an efficient alternative to state transition tensors for nonlinear uncertainty quantification. While previous directional state transition tensors used the…
Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
Tensors with unit Frobenius norm are fundamental objects in many fields, including scientific computing and quantum physics, which are able to represent normalized eigenvectors and pure quantum states. While the tensor train decomposition…
A notion of distorted torsion tensor was introduced by Okubo, in the establishment of the Nijenhuis-Bianchi identity and of BRST-like operators. These quantities are constructed with the help of the Nijenhuis tensor, which in turn is…
We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative…