Recent content by throw

Some heavy criticism of this whole approach here:

He explains why on the page, referencing equation (1.74). If you apply (1.75) to a four-vector and use ##\beta = 0## (what this implies for ##\sinh## and ##\cosh## is on p.18 explicitly too) you can see this explicitly.

I've already pointed out that only one idea of a path is being used in this thread, to see you argue that these four manifestations+examples of the (simple) idea of a path in a quantum and/or a classical context are all somehow radically different things that encode different fundamental ideas...

That's what I did when I cited multiple posts and argued they seem to be using only one notion of a 'path', you seem to be the only person here arguing there are multiple notions of a path (without any citations to justify this claim I might add). It's absolutely not an accepted fact that...

By a path is meant a curve which can be determined by a position vector at each instant, which can equivalently be given by knowing an initial position, a tangent vector (velocity/momentum) at that point, and a law which tells us how they evolve (with respect to e.g. time, or some other...

One should compare those words to those in the first sections of the earlier QM volume too. The idea that quantum objects have paths contradicts the very first thing QM says as one can see from the first section of both of these books.

Are you implying that the fact that continuous spectrum eigenfunction solutions of a Schrodinger equation are not square integrable, and so technically not in a Hilbert space (an issue that does not stop books like L&L), somehow let's us rationalize the existence of a time operator in a...

While Messiah has a separate section devoted to discussing various approaches to the continuous spectrum, he does not seem to discuss the approach I referenced, which is also the approach Dirac takes in his QM book. The continuous spectrum is implicit in just about everything one does in QFT...

This is just one possible interpretation of continuous spectrum eigenfunctions - it is not the only possible interpretation one can give to continuous spectrum eigenfunctions: There are plenty of books which take the alternative approach, for example Landau and Lifshitz 'Quantum Mechanics'...

In the non-relativistic case, time-energy uncertainty involves energy measurements at two different times, it's hard to believe this is from some operator relation since the whole reason for NRQM in the first place is the inability of simultaneously (i.e. at the same time) prescribing values of...

I would like to see Weinberg's perspective directly applied to the non-relativistic case as much as possible, the closest general reference seems to be Ballentine.

Unfortunately it's a bit shocking to read some of this discussion and I will try to push back on the sense I'm getting from it e.g. this focus on the NW operator is completely unjustifiable, or the apparent distinction between RQM and QFT in any serious sense, or the discussion about time...

Have a look at how L&L first introduce and then use an order parameter in book 5.

The action for a relativistic particle is ##S = - m \int ds = - m \int \sqrt{-\dot{x}^2} d \tau## This clearly assumes ##m \neq 0##, however we must also recognize that the system is a constrained system since ##p_{\mu}## satisfies ##p^2 = m^2##, so one should really first reformulate the...

This is a false dichotomy, one can set up a quantum field operator even for a single particle in non-relativistic quantum mechanics - they are usually introduced in a non-relativistic context for systems of identical particles by noting the matrix elements for transitions in such systems can be...