Bargmann-Fock space
The Bargmann-Fock space (or simply Fock space) is the Hilbert space^{} of entire functions^{}, ${\mathcal{F}}^{2}(\u2102)$ s.t.
$$ |
with associated inner product
$${\int}_{\u2102}F(z)\overline{G(z)}{e}^{-\pi {|z|}^{2}}\mathit{d}x\mathit{d}y$$ |
where $z=x+iy$
References
- 1 V. Bargmann, “Remarks on a Hilbert Space of Analytic Function^{}” Proceedings of the National Academy of Sciences of the United States of America 48 (1962): 199 - 204
- 2 V. Bargmann & I. T. Todorov, “Spaces of analytic functions on a complex cone as carriers for the symmetric tensor representations of SO(n)” Journal of Mathematical Physics 18 6 (1977): 1141 - 1148
Title | Bargmann-Fock space |
---|---|
Canonical name | BargmannFockSpace |
Date of creation | 2013-03-22 16:42:44 |
Last modified on | 2013-03-22 16:42:44 |
Owner | ErlendA (6587) |
Last modified by | ErlendA (6587) |
Numerical id | 14 |
Author | ErlendA (6587) |
Entry type | Definition |
Classification | msc 43A15 |
Synonym | Fock space |
Defines | Fock space |