An identity for T-ordered exponentials with applications to quantum mechanics |
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Authors: | Enrico Onofri |
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Institution: | Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540, USA |
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Abstract: | The solution of the Cauchy problem for Liouville's equation φxy = eφ is shown to be equivalent to the calculation of a T-ordered exponential of a two-dimensional variable matrix. This gives rise to an identity for the T-ordered exponential involving two arbitrary functions. The formalism is applied to the time evolution of a magnetic dipole in a time dependent magnetic field and to the one-dimensional Dirac equation with external potential tanh λx which is relevant for field theoretic applications. A generalization to n-dimensional matrices is also given. |
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