Segal–Bargmann Transforms Associated to a Family of Coupled Supersymmetries

  title={Segal–Bargmann Transforms Associated to a Family of Coupled Supersymmetries},
  author={Cameron L. Williams},
  journal={Complex Analysis and Operator Theory},
. The Segal-Bargmann transform is a Lie algebra and Hilbert space isomorphism between real and complex representations of the oscillator algebra. The Segal-Bargmann transform is useful in time-frequency analysis as it is closely related to the short-time Fourier transform. The Segal-Bargmann space provides a useful example of a reproducing kernel Hilbert space. Coupled supersymmetries (coupled SUSYs) are generalizations of the quantum harmonic oscillator that have a built-in supersymmetric… 



Segal–Bargmann and Weyl transforms on compact Lie groups

We present an elementary derivation of the reproducing kernel for invariant Fock spaces associated with compact Lie groups which, as Ólafsson and Ørsted showed in (Lie Theory and its Applicaitons in

Slice Segal–Bargmann transform

The Segal–Bargmann transform is a unitary map between the Schrödinger and Fock space, which is used, for example, to show the integrability of quantum Rabi models. Slice monogenic functions provide

Clifford Algebra-Valued Segal–Bargmann Transform and Taylor Isomorphism

Classical Segal-Bargmann theory studies three Hilbert space unitary isomorphisms that describe the wave-particle duality and the configuration space-phase space. In this work, we generalized these

The Segal–Bargmann Transform on a Symmetric Space of Compact Type☆

Abstract We study the Segal–Bargmann transform on a symmetric space X of compact type, mapping L 2 ( X ) into holomorphic functions on the complexification X C . We invert this transform by

The Segal-Bargmann "Coherent State" Transform for Compact Lie Groups

Abstract Let K be an arbitrary compact, connected Lie group. We describe on K an analog of the Segal-Bargmann "coherent state" transform, and we prove (Theorem 1) that this generalized coherent state

Coupled supersymmetry and ladder structures beyond the harmonic oscillator

ABSTRACT The development of supersymmetric (SUSY) quantum mechanics has shown that some of the insights based on the algebraic properties of ladder operators related to the quantum mechanical

A generalization of the Bargmann - Fock representation to supersymmetry

In the Bargmann - Fock representation the coordinates act as bosonic creation operators while the partial derivatives act as annihilation operators on holomorphic 0-forms as states of a D-dimensional

Geometric Quantization¶and the Generalized Segal--Bargmann Transform¶for Lie Groups of Compact Type

Abstract: Let K be a connected Lie group of compact type and let T*(K) be its cotangent bundle. This paper considers geometric quantization of T*(K), first using the vertical polarization and then

Coherent state transforms and the Weyl equation in Clifford analysis

We study a transform, inspired by coherent state transforms, from the Hilbert space of Clifford algebra valued square integrable functions L2(ℝm, dx) ⊗ ℂm to a Hilbert space of solutions of the Weyl