Your functions t[tau] and x[tau] depend on the value of a and you do not include a as an argument. Perhaps change those to t[a,tau] and x[a,tau]

The size of your terms rapidly decrease in your infinite summations and integrals. You might look at integrating and summing over -20 to 20 and -30 to 30 and -40 to 40 and see the results seem to get very close to each other and will not require infinite time to calculate. You might also increase the step size in the Table you are constructing for your ListLinePlot so that you can still see what you need, but do not take five times longer to complete.