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Il Nuovo Cimento A (1965-1970)

, Volume 48, Issue 1, pp 91–99 | Cite as

Canonical transformations and quantization of singular Lagrangian systems

  • L. Castellani
  • D. Dominici
  • G. Longhi
Article

Summary

In this work we propose a method of quantization for models described by singular Lagrangians. A set of variables, suitable for the quantization, is obtained by means of a canonical transformation. The quantum theory is carried out by working in the complete phase space; in other words, we do not eliminate the variables corresponding to the second-class constraints, as suggested by Dirac. The expectation values of the constraints are required to be zero and the problem of the consistency of these conditions is studied.

Riassunto

In questo lavoro si espone un metodo di quantizzazione per modelli descritti da lagrangiane singolari. Mediante una trasformazione canonica si ottiene un gruppo di variabili appropriate per la quantizzazione; questa è eseguita nel nuovo spazio delle fasi complete: non vengono cioè eliminate le variabili corrispondenti ai vincoli di seconda classe, come suggerito da Dirac. Si richiede che siano nulli i valori di aspettazione dei vincoli e si studia il problema della consistenza di tali condizioni.

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Copyright information

© Società Italiana di Fisica 1978

Authors and Affiliations

  • L. Castellani
    • 1
  • D. Dominici
    • 2
  • G. Longhi
    • 1
    • 2
  1. 1.Istituto di Fisica Teorica dell’UniversitàFirenze
  2. 2.Istituto Nazionale di Fisica NucleareSezione di FirenzeFirenzeItalia

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