Related papers: Vector coherent state representations and their in…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The…
The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Group representations play a central role in theoretical physics. In particular, in quantum mechanics unitary --- or, in general, projective unitary --- representations implement the action of an abstract symmetry group on physical states…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use…
The well-known canonical coherent states are expressed as an infinite series in powers of a complex number $z$ together with a positive sequence of real numbers $\rho(m)=m$. In this article, in analogy with the canonical coherent states, we…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
As a substantial generalization of the technique for constructing canonical and the related nonlinear and q-deformed coherent states, we present here a method for constructing vector coherent states in the same spirit. These vector coherent…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but…
A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with…
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of…
We generalise the notion of coherent states to arbitrary Lie algebras by making an analogy with the GNS construction in $C^*$-algebras. The method is illustrated with examples of semisimple and non-semisimple finite dimensional Lie algebras…
The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…