An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity |
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Authors: | Joseph I Goldman |
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Institution: | (1) Department of Physics, The American University, 20016 Washington, D.C.;(2) The Institute for Theoretical Studies, Berkeley, California |
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Abstract: | We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg
ik
(x) andg
00(x) with coordinate gaugeg
i0=0. The Hamiltonian of the system is found to be a linear function of –g
00(x)]1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc
2)H
(x)
,H
(x)
]=P
–
, whereH
(x)
is the Hamiltonian of the system, which is a linear functional of (x)–g
00(x)]1/2 andP
s(x)
represents the momentum-density operator averaged with the classical functions(x)]. |
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Keywords: | |
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