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Consider a vacuum of charged massless scalar field.

Then the uniform and isotropic electric field $E$ is turned on for a time interval $\tau$.

The question is, how many scalar particles are created?

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This question makes no sense. When one is talking of scalars the number is limited by their masses and the energy supplied, but there are no charged elementary scalars in the Standard Model of particle physics, let alone massless ones. Have a look at this question, which is talking of generating with an electric field out of the vacuum fermion pairs physics.stackexchange.com/questions/46697/… . There exists an experiment that found the effect of these pairs, link arxiv.org/abs/0901.2631 –  anna v Dec 15 '12 at 17:32
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@annav I would say the question does make sense, but as you said, it has a short and definite answer: "zero according to our current models." I say current models because maybe in principle you could produce some superpartners? (although given how hard it is to make an electron/positron this way, it might be a bit of an engineering challenge to produce the spartners!). –  twistor59 Dec 17 '12 at 7:40
    
Since you're clearly not talking about the standard model you need to define your model (by, say, giving its Lagrangian) before anyone can talk about it. But Schwinger pair production is a general thing which you should be able to compute straightforwardly - look it up. –  Michael Brown May 3 '13 at 8:51
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