Field operators and their spectral properties in finite-dimensional quantum field theory
Journal Article
·
· Found. Phys.; (United States)
In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states was V = C/sup r/. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables (L/sup 2/(R/sup r/,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We shall show that the isomorphism between the exponential of V and L/sup 2/(R/sup r/,dx) can be understood as the decomposition by generalized eigenvectors of field operators (''Fourier transform'').
- Research Organization:
- Department of Mathemtics and Computer Science, San Jose State University, San Jose, California 95192
- OSTI ID:
- 5547153
- Journal Information:
- Found. Phys.; (United States), Journal Name: Found. Phys.; (United States) Vol. 15:3; ISSN FNDPA
- Country of Publication:
- United States
- Language:
- English
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