A characterization of the Second Quantization by using the Segal duality transform

作者：Srivastava H M^*; Gonzalez B J; Negrin E R

来源：Applied Mathematics and Computation, 2013, 219(11): 6236-6240.

DOI：10.1016/j.amc.2012.11.080

• Duality principle
• Fourier-Wiener or Wiener transform
• Fourier-Plancherel transform
• Operators on Hilbert space
• Second Quantization
• Unitary extension
• Dominated Convergence Theorem
• Gaussian type integrals

The main object of this article is to establish the necessary and sufficient conditions in order to represent the Second Quantization in terms of a certain class of the Fourier-Wiener or the Wiener transforms via the Segal duality transform. We first analyze the finite-dimensional case and derive a matrix expression of this class of the Fourier-Wiener or the Wiener transforms. We then extend this analysis to derive the corresponding results for a certain family of the Fourier-Wiener or the Wiener transforms over Hilbert spaces.

• 出版日期2013-2-1