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5h
comment Is there a reason why the spin of particles is integer or half integer instead of even and odd?
The punchline then: Just like vectors and tensors, you can have these spin half things called spinors. The condition that all physical rules have to transform nicely under spacetime (Lorentz) transformations forces us to have only objects which transform as mentioned above. Beyond that, the convention for spins is such that $2 \pi$ represents a "full rotation". Unless you want to mess around with that, you don't want to redefine scaled charges.
5h
comment Is there a reason why the spin of particles is integer or half integer instead of even and odd?
Ah, I see. I'm sorry about that. If you do a typical undergraduate course on classical mechanics (meant for physicists), you might learn enough about Lagrangians, Hamiltonians, symmetries and "generators" to get the flavour of my answer. If you follow that up with an undergraduate course on quantum mechanics, then hopefully my answer will make sense.
15h
comment Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?
Gauge theories have Ward identities. So yes, your amplitude might naively have spacetime indices, but when you contract it with the polarization vectors of the gluons, the spurious dependence is supposed to vanish (transverse modes, little group, etc).
15h
comment Can quantum vacuum carry entropy?
@MrFermiMr: What do you mean by entropy? How do you define it?
15h
comment Can quantum vacuum carry entropy?
@Bubble: That's a technically correct statement, but slightly naive. Eg: Consider one of the Bell states: each of them is a "pure" state. But when we try to split the system into its two component electrons, each of their reduced states is mixed, due to their entanglement -- this results in some entanglement entrop, based on your formula below. So it's important to ask entanglement between which two components.
15h
comment Is there a reason why the spin of particles is integer or half integer instead of even and odd?
@Erbureth: Recall that (even in classical mechanics) "angular momentum" is the generator of rotations. So if I start using units of $\tau = 2 \pi$ to represent a half rotation (instead of $\pi$) then the values of charge will halve to maintain the value of $e^{i q \theta}$
15h
comment Is there a reason why the spin of particles is integer or half integer instead of even and odd?
@ratchetfreak: Oops! Fixed. Thanks.
15h
revised Is there a reason why the spin of particles is integer or half integer instead of even and odd?
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1d
revised Is there a reason why the spin of particles is integer or half integer instead of even and odd?
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1d
revised Is there a reason why the spin of particles is integer or half integer instead of even and odd?
added 189 characters in body
1d
answered Is there a reason why the spin of particles is integer or half integer instead of even and odd?
1d
comment Renormalization condition: why must be the residue of the propagator be 1
@innisfree: Yeah, I think your answer shows the calculational aspects of how this comes about. On a related note, it seems that authors usually state that we like to have unit residue to make the propagator look like a "free-field" one. Wanting asymptotic states to look like "free" particles imposes the required normalization for $\langle \phi^\dagger \phi \rangle$.
Sep
12
comment How exact is the analogy between statistical mechanics and quantum field theory?
There are insights to be gained into QFT by looking at the analytic structure of S-matrix elements and such things. I would suspect that those results would be altered due to the Wick rotation -- while insights based on formal reasong using path integrals might carry over more easily. Just my 2 cents of thinking out loud.
Sep
11
reviewed Edit suggested edit on Why can interactions be neglected for the Integer Quantum Hall effect?
Sep
11
revised Why can interactions be neglected for the Integer Quantum Hall effect?
corrected spelling the name of C.-A. de Coulomb; cmp. http://en.wikipedia.org/wiki/Coulomb_interaction
Sep
8
revised S-Matrix and normalization of states
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Sep
8
revised Fundamental representation in quantum field theory
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Sep
8
comment S-Matrix and normalization of states
Unitarity ensures that "probability is conserved" i.e. the probability interpretation a la Born's rule continues to make sense. Changing normalization of states is not a problem, since physical answers always look like $\dfrac{\langle s|U^\dagger U|s\rangle}{\langle s|s\rangle}$
Sep
7
revised Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch
edited title
Sep
6
comment Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch
Might be a little too simplistic, but here's a blog post I wrote. If you understand what a "gauge-covariant derivative" is, you can make sense of the treatment in almost any textbook. You could (for eg) have a look at section IV.6 in Zee's book QFT in a nutshell, or almost any QFT notes you find online.