Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Hamiltonian and Diffeomorphism Generators of a Quantum Field in R x S^2 Spacetime

Document Type : Original Article

Author
Department of Physics, Isfahan University of Technology, Isfahan, Iran
Abstract
Within the ADM formalism, spacetime is foliated by spacelike hypersurfaces, dividing spacetime into space and time. In this formalism, the evolution of fields can be separated into evolution on these hypersurfaces and evolution from one hypersurface to the next. The commutators of these generators form an algebra known as the Dirac Algebra or hypersurface deformation algebra. In this paper, we expand the matter field on the 3-dimensional R x S^2 spacetime using the basis of spherical harmonics on S^2. Inspired by the approach of second quantization, we promote the coefficients of this expansion to creation and annihilation operators. We demonstrate that the algebra of the evolution generators, determines the Hamiltonian and diffeomorphism generators on S^2. The tensor character of the matter field is classified based on its Lie derivative with respect to its diffeomorphism generators. This quantization method determines the ordering of creation and annihilation operators in the evolution generators.
Keywords
Subjects

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Volume 2, Issue 3
Summer 2025
Pages 123-127

  • Receive Date 09 July 2025
  • Revise Date 15 July 2025
  • Accept Date 18 August 2025
  • First Publish Date 18 August 2025
  • Publish Date 01 August 2025