https://doi.org/10.1140/epjp/i2011-11131-8
Regular Article
Canonical analysis of scalar fields in two-dimensional curved space
1
Department of Applied Mathematics, The University of Western Ontario, N6A 5B7, London, ON, Canada
2
Department of Mathematics and Computer Science, Algoma University, P6A 2G4, Sault St. Marie, ON, Canada
* e-mail: dgmckeo2@uwo.ca
Received:
20
July
2011
Revised:
16
September
2011
Accepted:
26
October
2011
Published online:
27
December
2011
Scalar fields on a two-dimensional curved surface are considered and the canonical structure of this theory analyzed. Both the first- and second-order forms of the Einstein-Hilbert (EH) action for the metric are used (these being inequivalent in two dimensions). The Dirac constraint formalism is used to find the generator of the gauge transformation, using the formalisms of Henneaux, Teitelboim and Zanelli (HTZ) and of Castellani (C). The HTZ formalism is slightly modified in the case of the first-order EH action to accommodate the gauge transformation of the metric; this gauge transformation is unusual as it mixes the affine connection with the scalar field.
© Società Italiana di Fisica and Springer, 2011
