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Doctoral Thesis
DOI
10.11606/T.43.1999.tde-04122013-141239
Document
Author
Full name
Sebastião Cassemiro de Figueiredo Filho
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1999
Supervisor
Committee
Rivelles, Victor de Oliveira (President)
Fleming, Henrique
Frenkel, Josif
Helayël- Neto, José Abdalla
Zimerman, Abraham Hirsz
Title in Portuguese
Análise Hamiltoniana e Quantização da Teoria de Gravitação Dilatônica em Duas Dimensões
Keywords in Portuguese
Física de partículas
Gravidade
Abstract in Portuguese
Neste trabalho, analisamos o modelo de gravitação dilatônica proposto por Callan, Giddings, Harvey e Strominger (modelo de CGHS). Aplicamos a teoria de vínculos ao modelo e mostramos que só existem vínculos de primeira classe. Em seguida ap0licamos a técnica de BRST-BFV para quantizar a teoria. Mostramos que os fantasmas na função de partição estão desacoplados dos campos e podem ser integrados. Utilizamos uma transformação canônica para escrever os vínculos na forma quadrática, que facilita a quantização da teoria. Para completar a quantização usamos o procedimento de Dirac para obter a álgebra dos vínculos expressa na forma do tensor momento-energia. Existe uma anomalia na álgebra que é apropriadamente eliminada quando adicionamos um termo de improvement à ação. Finalmente usamos o procedimento de Dirac para obter soluções para a função de onda. Isto prova que a teoria de CGHS em duas dimensões é perfeitamente quantizável.
Title in English
Hamiltonian analysis and quantization of dilatonic gravitational theory in two dimensions
Keywords in English
Gravity
Particle physics
Abstract in English
We analyse a theory of gravitation in two dimensions using the hamiltonian formalism. For this purpose we use the CGHS model in the conformal gauge. The theory of constraints shows that we have only first-class constraints. After that, we apply the BRST-BFV technique to quantize the theory. We show that the ghosts in the partition function are decoupled from the fields. Then we integrate the ghosts in the partition function. By a suitable canonical transformation we write the constraints in a quadratic form which facilitates the quantization of the theory. To complete the quantization we use the Dirac procedure to obtain the constraints algebra expressed in the energy-momentum tensor form. There is an anomaly in the algebra which can be suitably eliminated by the addition of an improvement term in the action. Finally we use the Dirac procedure tro obtain solutions for the wave function. This proves that the CGHS theory in two dimensions is quantizable.
 
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Publishing Date
2014-02-18
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • CASSEMIRO, F. F. S., and RIVELLES, V. O. Canonical And Functional Schrodinger Quantization Of Two-Dimensional Dilaton Gravity. Physics Letters. Section B, 1999, vol. 452, p. 234.
All rights of the thesis/dissertation are from the authors
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