### Abstract

It is shown that, already for source-free Maxwell fields, one can construct observable algebras which in the classical theory are on the "same footing" as the one normally used but which in the quantum theory cannot be represented by operators on the standard Fock space. Thus, in quantum field theory there is a genuine freedom in the choice of the operator algebra over and above the well-known freedom in the choice of the representation of a given algebra. This freedom is likely to play an important role in non-perturbative treatments of non-abelian theories.

Original language | English (US) |
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Pages (from-to) | 393-398 |

Number of pages | 6 |

Journal | Physics Letters B |

Volume | 274 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 16 1992 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*274*(3-4), 393-398. https://doi.org/10.1016/0370-2693(92)92004-Z

}

*Physics Letters B*, vol. 274, no. 3-4, pp. 393-398. https://doi.org/10.1016/0370-2693(92)92004-Z

**Inequivalent observable algebras. Another ambiguity in field quantisation.** / Ashtekar, Abhay; Isham, C. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Inequivalent observable algebras. Another ambiguity in field quantisation

AU - Ashtekar, Abhay

AU - Isham, C. J.

PY - 1992/1/16

Y1 - 1992/1/16

N2 - It is shown that, already for source-free Maxwell fields, one can construct observable algebras which in the classical theory are on the "same footing" as the one normally used but which in the quantum theory cannot be represented by operators on the standard Fock space. Thus, in quantum field theory there is a genuine freedom in the choice of the operator algebra over and above the well-known freedom in the choice of the representation of a given algebra. This freedom is likely to play an important role in non-perturbative treatments of non-abelian theories.

AB - It is shown that, already for source-free Maxwell fields, one can construct observable algebras which in the classical theory are on the "same footing" as the one normally used but which in the quantum theory cannot be represented by operators on the standard Fock space. Thus, in quantum field theory there is a genuine freedom in the choice of the operator algebra over and above the well-known freedom in the choice of the representation of a given algebra. This freedom is likely to play an important role in non-perturbative treatments of non-abelian theories.

UR - http://www.scopus.com/inward/record.url?scp=0000387219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000387219&partnerID=8YFLogxK

U2 - 10.1016/0370-2693(92)92004-Z

DO - 10.1016/0370-2693(92)92004-Z

M3 - Article

AN - SCOPUS:0000387219

VL - 274

SP - 393

EP - 398

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3-4

ER -