Recent content by Phiphy

Non-locality happens when there are negative powers of momentum in the lagrangian. A finite series of positive powers of momentum is still local. There must be some other physical reasons to rule out higher powers of momentum.

When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of \phi, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM...

No. The rest mass afterwards only need to be less than the total energy of the initial particles. You can accelerate very light particles, eg., electrons, to get large kinetic energy and produce heavy particles in the end.

That's a clear picture of the strategy. Thank you again, GreyBadger.

Just add each component respectively: a+ib=(1+0i,0+i,0+0i)=(1,i,0). You can not imagine its direction in real 3-space because complex numbers can not be ordered. But you can imagine a 6-dimensional vector with a definite direction.

JavierR: I think you are right. That explains why causality requires commutator=0 for space-like separations. But I am still trying to figure out a rigid proof of the inverse, ie., commutator=0 for space-like separattions => causality is respected. Hans: Although I did not understand how you...

Thank you for the explanation. So if we want to go from SM theory to hadron collider phenomena, what is the commonly used strategy? As I understand it, we first need to know the PDF of the proton, then calculate parton collision cross-section, then use parton shower to calculate jet production...

The Feynman propagator in QFT is not zero for space-like separation, but we say this does not mean that causality is violated, we should check the commutator of field operators instead, and the commutators vanish for space-like separation. My question is: why do we use commutators to check...

What is "parton shower"? I only know that parton shower is an algorithm of calculating QCD processes on the collider. Can anyone give me a brief introduction on the purpose and basic ideas of parton shower? Thanks.

I think the statement that "energy is not conserved for a virtual particle" is not right. The 4-momentum including energy is always conserved as the requirement of Lorentz covariance. This is manifest in Feynman diagrams: when we go from the space-time representation to momentum representation...

Thank you, Humanino. I read this paper one year ago, however I did not fully understand it. Think I should read it again.

In fact I am very glad to see that QFT must break down at some point. Maybe my question is too conceptual to get a concrete answer. Let's just leave it as it is. A different but related question: Can anyone remind me why gravity cannot be quantized as a field theory? Is there any simple...

Yep, I was just trying to guess the meaning of the sentence. And I guess the OP's book may well be a popular science book. I agree that it is too sloppy to make a statement like this using the not well defined terms like "long range".

Thank you for mentioning A Zee. It was exactly what he said in his book(QFT in a Nutshell) made me bring up this question. I still don't understand why this "divergence" criterion is reasonable. Let's put it in this way. I remember Zee also said in his book, "theories in physics have the...

The usual perception is quantum field theory is not fundamental since it has divergence. A fundamental theory must always be finite, like string theory. But in the physical sense, a fundamental theory means it is valid at any arbitrary energy scale. We know that non-renormalizable theories...