Recent content by kharranger

Let f be a differentiable complex valued function on R. If f is square integrable, then it is not the case that f(x) must approach zero at infinity. counterexample: f(x)=x^2 exp(-x^8 sin^2(20x)). If I also require that the derivative of f be square integrable, is that enough to guarantee that...

You can take it to mean that the N-th partials all exist and are continuous.

I would also argue that the problem of time is not really a problem to the same degree as non-renormalizability. The problem of time just reflects the fact that gravity is a gauge theory, and as in any gauge theory we use a gauge invariant description because we are too stupid to think up...

I believe you can think of the vacuum in this case as carrying a projective representation of the Lorentz group. The state is a not part of a 4-vector, but it is not invariant under a lorentz transformation; it changes by a phase. In building perturbation theory about this state you would in...

I think causality and measurment are not the reason for space-like commutation. We never measure eigenstates of the field operator. We measure only asymptotic particle states. The reason for space-like commutation is really lorentz invariance. When you introduce interactions, the S-matrix in...

If they are stable, they would not be detectable and would appear as missing energy in a collision. If not, they would decay into other particles which could be detectable.

Nothing disastrous can possibly happen at LHC. This is because cosmic rays with energies equal to and far larger than LHC particle energies are hitting the Earth's atmosphere all the time, so if any doomsday type thing could happen, it already would have happened.

The internal dimensions should not be externally frozen. Their size and shape should be determined dynamically by the theory.

That's right, there's no problem quantizing gravity per se. The problem is that the resulting quantum field theory is not renormalizable so it is not valid at arbitrarily high energy scales.

Yes, if you vary the metric+connection EH action with respect to the connection, you find the algebraic equation: connection=levi-civita connection. Thus you can insert these equations of motion inside the action, recovering the metric-only EH action, and the two are classically equivalent.

The quantum equivalent of the EL equations are the Schwinger-Dyson equations, which say that the EL equations hold as operator equations in expectations values.

String theory is based on the same old quantum mechanics as all other theories. There is no problem quantizing gravity per se, the only catch is that the resulting field theory is an effective theory, only valid at energies below the Planck scale. What's different about string theory is that...

Suppose I want to bypass the entire Hamiltonian formulation of quantum field theory and define the theory using a path integral. Thus all I can calculate are Green's function which are time ordered products of local operators. Given only these (no expansions of the field in creation...

The path integral is useful for visualizing, setting up and organizing a perturbative calculation. That's what feynman diagrams are, just perturbative calculation of some path integral that gives very useful approximate answers.

yes they should probably be taught separately. QFT happens to be the most dominant and useful tool to explain particles, but it is also useful in other realms.