Saturday, 2 March 2019

Exercise 2.10 Maxwells equations in 2-dimensional spacetime

Question

Consider Maxwell's equations, d= 0 , d*= *J in 2-dimensional spacetime. Explain why one of the two equations can be discarded. Show that the electro-magnetic field can be expressed in terms of a scalar field. Write out the field equations for this scalar field in component form.

Answer 

"2-dimensional spacetime"? Is that one dimension of space and another of time or two space and one time? We assume the former and see what happens.

This question seemed too easy, especially after my labours on Maxwell's equation with three-forms. In one time and one space dimension, the first of Maxwell's equations becomes 0 = 0 and I think that the second produced the scalar field which I wrote down in almost one page: Ex 2.10 Maxwells equations in 2-dimensional spacetime.pdf.

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