Quantum Field Theory: An Introduction For Chemical Physicists by Porter Richard N;

Author:Porter, Richard N;
Language: eng
Format: epub
Publisher: World Scientific Publishing Company
Published: 2022-12-15T00:00:00+00:00

where we have ignored the term in Eq. (4.61) because for a Dirac field, Eqs. (5.62) and (5.64) show that The energy density is thus given by

and the Hamiltonian is

A more useful form for the Hamiltonian is obtained by making use of Eq. (5.53) to write

whereupon Eq. (5.70) becomes in the γμ notation

Similarly, the total particle momentum is that is,

To find the expression for the charge-current density, we proceed as for complex scalar quantum fields, but now with the Lagrangian given in Eq. (5.63). First, we introduce a global phase shift α by making the replacements6

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