- #1
Katie3
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The question is as follows;
'A free quantum field theory is related to an infinite number of quantum mechanical harmonic oscillators as unit mass particles on springs with spring constants k, where k takes all values. Now imagine the following scenario: these particles also have non-zero charges, and I suspend the system in a constant electric field Eo. Ignoring the effects of any outgoing radiations due to the oscillations of charged particles, show that this system of harmonic oscillators is equivalent to a massive scalar field theory with a classical source term int(d^4x J*(phi)). Where J is the source and phi is the scalar field. Find the connection between Eo and J.
I've been working on this all day and I feel like I've gotten no where. It *should* be an easy question. If someone could point me in the right direction, that would be great!
'A free quantum field theory is related to an infinite number of quantum mechanical harmonic oscillators as unit mass particles on springs with spring constants k, where k takes all values. Now imagine the following scenario: these particles also have non-zero charges, and I suspend the system in a constant electric field Eo. Ignoring the effects of any outgoing radiations due to the oscillations of charged particles, show that this system of harmonic oscillators is equivalent to a massive scalar field theory with a classical source term int(d^4x J*(phi)). Where J is the source and phi is the scalar field. Find the connection between Eo and J.
I've been working on this all day and I feel like I've gotten no where. It *should* be an easy question. If someone could point me in the right direction, that would be great!