# Bargmann-Fock space

The Bargmann-Fock space (or simply Fock space) is the Hilbert space of entire functions, $\mathcal{F}^{2}(\mathbb{C})$ s.t.

 $\int_{\mathbb{C}}|F(z)|^{2}e^{-\pi|z|^{2}}dxdy<\infty$

with associated inner product

 $\int_{\mathbb{C}}F(z)\overline{G(z)}e^{-\pi|z|^{2}}dxdy$

where $z=x+iy$

## References

• 1 V. Bargmann, “Remarks on a Hilbert Space of Analytic FunctionProceedings 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 BargmannFockSpace 2013-03-22 16:42:44 2013-03-22 16:42:44 ErlendA (6587) ErlendA (6587) 14 ErlendA (6587) Definition msc 43A15 Fock space Fock space