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Difference between revisions of "Creation operators"

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A family of closed linear operators <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027020/c0270201.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027020/c0270202.png" /> is some Hilbert space, acting in the [[Fock space|Fock space]] constructed over <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027020/c0270203.png" />. They are the adjoints of the [[Annihilation operators|annihilation operators]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027020/c0270204.png" />.
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A family of closed linear operators $\{ a^*(f) : f \in H \}$, where $H$ is some [[Hilbert space]], acting in the [[Fock space]] constructed over $H$. They are the adjoints of the [[annihilation operators]] $\{ a(f) : f \in H \}$.
  
  
  
 
====Comments====
 
====Comments====
Cf. [[Annihilation operators|Annihilation operators]] for a precise description of the operators <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c027/c027020/c0270205.png" /> and for suitable references.
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Cf. [[Annihilation operators]] for a precise description of the operators $a^*(f)$ and for suitable references.

Revision as of 19:40, 9 December 2014

A family of closed linear operators $\{ a^*(f) : f \in H \}$, where $H$ is some Hilbert space, acting in the Fock space constructed over $H$. They are the adjoints of the annihilation operators $\{ a(f) : f \in H \}$.


Comments

Cf. Annihilation operators for a precise description of the operators $a^*(f)$ and for suitable references.

How to Cite This Entry:
Creation operators. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Creation_operators&oldid=35529
This article was adapted from an original article by R.A. Minlos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article