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alfredblase

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Three related problems in this one.

1. Show that: [tex]\frac{\partial}{\partial t} \int_{t'}^t d\tau V \left (\mathbf{q'}+ \frac{\tau-t'}{t-t'} \mathbf{q-q'},\tau \right )=V \left (\mathbf{q},t \right ) + \int_{t'}^t d\tau \frac{\partial}{\partial t}V \left (\mathbf{q'}+ \frac{\tau-t'}{t-t'}\mathbf{q-q'},\tau \right )[/tex]

where [tex]\frac{\partial \tau}{\partial t}\neq 0[/tex].

2. Whats is [tex]A_i[/tex]?

3. Show that [tex]\frac{\partial V}{\partial A_i}=\nabla_{q_i} V\frac{t-t'}{\tau-t'}[/tex]

They are probelms that I need to solve in reading a QFT text (Jean Zinn Justin p 22)

1. Show that: [tex]\frac{\partial}{\partial t} \int_{t'}^t d\tau V \left (\mathbf{q'}+ \frac{\tau-t'}{t-t'} \mathbf{q-q'},\tau \right )=V \left (\mathbf{q},t \right ) + \int_{t'}^t d\tau \frac{\partial}{\partial t}V \left (\mathbf{q'}+ \frac{\tau-t'}{t-t'}\mathbf{q-q'},\tau \right )[/tex]

where [tex]\frac{\partial \tau}{\partial t}\neq 0[/tex].

2. Whats is [tex]A_i[/tex]?

3. Show that [tex]\frac{\partial V}{\partial A_i}=\nabla_{q_i} V\frac{t-t'}{\tau-t'}[/tex]

They are probelms that I need to solve in reading a QFT text (Jean Zinn Justin p 22)

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