Suppose we have an integral $$Z(\lambda) = \frac{1}{\sqrt{2\pi}}\int^{+\infty}_{-\infty} dx e^{-\frac{x^2}{2!}-\frac{\lambda}{4!}x^4}.$$ To my knowledge this is a possible integral which can arise in QFT. My question is on the convergence of this integral. For what $\lambda$ will this integral be...

In the explanation of tides on earth there seem to be different versions for the second water bulge on the side opposite to the moon, while everybody seems to agree that the bulge on the moon side is due to the gravitational pull of the moon, I found the following explanations for the second bulg...

When studying gauge theory, I often see the statement that gauge invariance does not allow the Lagrangian of the theory to contain terms that are quadratic in the gauge field. For example, to quote Folland's book on quantum field theory (page 295): ...gauge invariance forbids the inclusion of te...

Suppose we have an air column closed at one end and open at one end. We know, the general formula for the wavelength of the stationary waves of different harmonics will be equal to $4L/n$. My confusion is, in this equation there is no speed of wave involved. Why not though? How does this make sen...