- #1

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## Homework Statement

My question is just about a small mathematical detail, but I'll give some context anyways.

(From Rubakov Sec. 2.2)

An expression for energy is given by

[tex] E= \int{}d^3x\frac{\delta{}L}{\delta{}\dot{\phi}(\vec{x})}\dot{\phi}(\vec{x}) - L,

[/tex]

where L is the Lagrangian,

[tex]

L=\int{}d^3{}x(\frac{1}{2}\dot{\phi}^2-\frac{1}{2}\partial_i\phi\partial_i\phi-\frac{m^2}{2}\phi^2).

[/tex]

To derive the expression for energy, Rubakov says that

[tex]

\frac{\delta{}L}{\delta{}\dot{\phi}(\vec{x})}=\dot{\phi}(\vec{x}).

[/tex]

What I want to know is, simply, how does he get this expression for

[tex]

\frac{\delta{}L}{\delta{}\dot{\phi}(\vec{x})}

[/tex]?

## Homework Equations

## The Attempt at a Solution

If I evaluate the expression, I just get

[tex]

\delta{}L=\int{}d^3x(\dot{\phi}).

[/tex]

Where'd the integral go in Rubakov's expression?