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age 29
visits member for 2 years
seen Jul 20 at 21:38

As time goes on, I grow more disillusioned with quantum field theory.


Jul
15
comment How to replace $T$-product with retarded commutator in LSZ formula?
I believe there is a related mistake: in integrating by parts, you didn't include the surface terms. Especially important is from the time variable e.g. $\langle\varphi^\dagger(y)\varphi(x)\rangle\big|_{x^0=-\infty}^{x^0=+\infty} = \langle\varphi^\dagger(y)\big(\varphi_\text{out}(x)-\varphi_\text{in}(x)\big) \rangle$. Neglecting it, you can show all amplitudes vanish. See the remark on page 206, line 9-10 of Itzykson and Zuber.
Jul
15
comment How to replace $T$-product with retarded commutator in LSZ formula?
Thanks! I am working through the details, but can’t understand why $q_1^0$ and $\omega_{q,A}$ etc are distinguished. They must be equal since $A$ is an external particle on its mass shell.
Jul
14
revised How to replace $T$-product with retarded commutator in LSZ formula?
set equation number in tag.
Jul
12
revised Electrostatics with Yukawa mass
Corrected a typo in the last equation.
Jul
12
comment Electrostatics with Yukawa mass
Yes that's right, thanks! This final piece of information implies $C=-\big[\rho e^{-\mu R} (\mu R+1)\big]/\big[2 \mu^3\big]$.
Jul
12
asked Electrostatics with Yukawa mass
Jul
11
comment Fourier expansion of the Klein-Gordon field
Also, it is easiest to quantize decoupled oscillators. By going to Fourier space, all the modes are decoupled, and the expansion coefficients are easily seen to satisfy the standard SHO algebra.
Jul
10
awarded  Yearling
Jul
9
revised How to replace $T$-product with retarded commutator in LSZ formula?
edited body
Jul
9
comment How to replace $T$-product with retarded commutator in LSZ formula?
This can't be right. Firstly, I don't understand why you say that in my case I have $x^0 < y^0$. This ordering was not simply chosen on a whim; it is somehow fixed by the fact that $q_1$ and $q_2$ are in the forward light-cone, but the reason eludes me. Secondly, the fields appearing in the reduction formula eq 5-169 above are full Heisenberg-picture fields. I have a problem with your use of Wick's theorem in that they only apply to interaction-picture fields (where they evolve according to the free part of the Hamiltonian), and is applicable in perturbation theory exclusively.
Jul
8
comment Why Are Even and Odd Regge Trajectories Degenerate?
possible duplicate of Why are the even and odd Regge trajectories degenerate?
Jul
7
revised How to replace $T$-product with retarded commutator in LSZ formula?
fixed gramatical error
Jul
6
accepted Nuclear Compton Scattering Data
Jul
6
asked How to replace $T$-product with retarded commutator in LSZ formula?
Jul
5
asked Nuclear Compton Scattering Data
Jul
2
comment Particle/Pole correspondence in QFT Green's functions
It seem that the word 'particles' is getting in the way. Let me state my question without using that word: "How do I prove that each pole on the real axis of Green's functions directly corresponds to an eigenvalue of the field theoretic Hamiltonian?"
Jul
2
comment Particle/Pole correspondence in QFT Green's functions
Just to add extra information, it is possible to show within non-relativistic potential scattering theory (for well-behaved potentials) the particle/pole correspondence both ways: essentially, existence of zeros of the Jost function establishes that wavefunctions will give a normalizable bound state, and also would give a pole on the real axis of the corresponding partial wave $s$-matrix eigenvalue. What is the generalization of this to relativistic field theory?
Jul
2
comment Particle/Pole correspondence in QFT Green's functions
I am perfectly aware of this technicality, and for that reason I refer, in the question, only to poles on the real axis, which correspond to strictly stable particles. Also, I am looking for a non-perturbative argument (possibly involving axiomatic field theory) for poles corresponding to particles.
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious