In this paper, we define invariant tensor product and study invariant tensor products associated with discrete series representations. Let G(V1) × G(V2) be a pair of classical groups diagonally embedded in G(V1 ⊕ V2). Suppose that dimV1 < dimV2. Let π be a discrete series representation of G(V1 ⊕ V2). We prove that the functor π⊗G(V1) maps unitary representations of G(V1) to unitary representat...

Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...

Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters...

We define a class of tensor network states for spin systems where the individual tensors are functionals fields. The construction is based on path integral representation correlators operators in quantum field theory. These infinite dimensional versions matrix product and projected entangled pair states. find field-tensor that generates Haldane-Shastry wave function extend it to two dimensions....

We first demonstrate how to construct a transfinite interpolation on a simplex of arbitrary dimension d. The inputs are (d + 1) functions describing the simplicial faces of decremented dimension (d − 1). We deduce the explicit expressions for tetrahedra and triangles by using the CGNS convention for the enumeration of topological entities. Second, our construction is applied to hypercubes as we...

A new type of topological matter interactions involving second–rank antisymmetric tensor matter fields with an underlying NT ≧ 1 topological supersymmetry are proposed. The construction of the 4–dimensional, NT = 1 Donaldson–Witten theory, the NT = 1 super–BF model and the NT = 2 topological B–model with tensor matter are explicitly worked out.