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Irreducible bilinear tensorial concomitants of an arbitrary complex antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In addition these bilinear concomitants are symmetric (or antisymmetric), self-dual (or anti-self-dual), and hermitian forms in the antisymmetric tensor. An important example of an antisymmetric valence-2 tensor, or bivector, is the electromagnetic field strength tensor which ordinarily is taken to be real-valued. In generalizing to complex-valued bivectors, the authors find the hermitian fo
In this paper, we present an eleven invariant isotropic irreducible function basis of a third order three-dimensional symmetric tensor. This irreducible function basis is a proper subset of the Olive-Auffray minimal isotropic integrity basis of that
This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the asymptotics
Birkhoffs theorem tells that any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. A similar theorem reveals that any unitary matrix can be decomposed as a weighted sum of complex permutation matrices. Unitary matr
It was shown recently that Birkhoffs theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.
In 2017, Lienert and Tumulka proved Borns rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Borns rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolut