Realization of a unique time evolution unitary operator in Klein Gordon theory |
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Authors: | T S Balasubranian Sunil kr Bhatia |
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Institution: | (1) Department of Mathematics, Banaras Hindu University, 221005 Varanasi, India |
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Abstract: | The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered.
Using the Klein Gordon equation formulated in the Hubert spaceL
2(R
3) and the Einstein’s relativistic equation in the spaceL
2(R
3, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL
2(R
3) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite
dimensional Hubert spaceL
2(R
3). |
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Keywords: | Physical vacuum states linearized Klein Gordon equation linearized Einstein’ s relativistic equation symplectic operator |
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