snoopies622
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- How are phi and psi (solutions to the Klein-Gordon and Dirac equations) expressed mathematically in quantum field theory?
I found a copy of David McMahon's "Quantum Field Theory Demystified" and I'm already confused on page 4 where he says, " . . in order to be truly compatible with special relativity, we need to discard the notion that \phi and \psi in the Klein-Gordon and Dirac equations respectively describe single particle states. In their place, we propose the following new ideas:
— The wave functions \phi and \psi are not wave functions at all, instead they are fields.
— The fields are operators that can create new particles and destroy particles."
As i understand things,
— the \psi in the Schrodinger equation represents a complex number at every point in space and time, while in the Dirac equation represents four complex numbers at every point in space and time. (I don't know what the \phi in the Klein-Gordon equation represents, but I'm guessing something similar.)
— an operator is something that changes a function into a different function. One way to think about it is - if a function is a vertical list of n complex numbers, then an operator is an nxn matrix that can be multiplied by the column of n numbers to produce a different column of n numbers.
In quantum field theory, what exists at every point in space and time? A matrix? More than one matrix?
— The wave functions \phi and \psi are not wave functions at all, instead they are fields.
— The fields are operators that can create new particles and destroy particles."
As i understand things,
— the \psi in the Schrodinger equation represents a complex number at every point in space and time, while in the Dirac equation represents four complex numbers at every point in space and time. (I don't know what the \phi in the Klein-Gordon equation represents, but I'm guessing something similar.)
— an operator is something that changes a function into a different function. One way to think about it is - if a function is a vertical list of n complex numbers, then an operator is an nxn matrix that can be multiplied by the column of n numbers to produce a different column of n numbers.
In quantum field theory, what exists at every point in space and time? A matrix? More than one matrix?
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