Conservation Laws and Symmetries

Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as |ψ⟩). If this quantity is conserved, in the meaning that the associated operator ˆD is constant: dˆDdt=0 it has to commute with the Hamiltonian operator ˆH. To prove this, in the Heisenberg picture of Classical QM, … Read more

Is single photon annihination of electron-positron pair prohibited by Feynman diagram analysis?

It is obvious that electron-positron pair cannot annihilate to a single photon which will violate the momentum conservation. My question is can we get this knowledge from Feynman diagram or perturbative expansion of QED? If we can’t, how can we make sure not to over-count diagrams when we draw Feynman diagram to compute the scattering … Read more

QFT and violation of Heisenberg uncertainty principle

In some QFT books is said that a free electron can emit a virtual photon as long as it reabsorbs the photon and returns to its original state within a time: Δt<ℏ2ΔE That inequality DOES VIOLATE the Heisenberg Uncertainty Principle. Why is that POSSIBLE? If it were said in a time Δt≥ℏ2ΔE I would not … Read more

Weinberg soft photon integral

In deriving the rate of emission of arbitrary numbers of soft photons in a general QED process, Weinberg performs the following integral (equations 13.2.8-9): −π(→pm⋅→pn)∫λ≤|→q|≤Λd3→q|→q|3(En−ˆq⋅→pn)(Em−ˆq⋅→pm)=2π2βnmln(1+βnm1−βnm)ln(Λλ) where β=√1−m2nm2m(→pn⋅→pm)2. I am trying to compute this integral for myself but am having some trouble with the angular integral. Would someone mind giving me some assistance? Answer I think … Read more

Is there any SU(∞)SU(\infty) gauge theory in quantum field theory?

The groups U(N) and SU(N) are the most important Lie groups in quantum field theory. The most popular are the U(1),SU(2),SU(3) groups (these gauge groups form the Standard model). But is there mentioned a SU(∞) gauge theory in physics literature? An example of such a theory could be the following: May be g∈SU(∞) smooth and … Read more

Can light absorb energy?

Everybody knows that all physics systems absorb light quanta, any material thing can absorb light quanta. But the reverse question is , can light absorb energy and therefore changes its frequency? If not, please give me some fundamentals or equations that prohibit this from happening. Answer The process of inverse Compton scattering does exactly this. … Read more

How can I make this toy quantum random walk model unitary?

Take a toy (1+1)-dimensional lattice model of the universe. A particle begins at x=0 at t=0. It has an amplitude 1/√2 to move one step to the left and amplitude 1/√2 to move one step to the right. At time t=1 it will either be at x=−1 or x=+1 with probability 12 each. At time … Read more

Relationship between lesser Green’s function and greater Green’s function in Keldysh formalism

I wonder if there is any general relationship between lesser Green’s function G<(t,t′) and G>(t,t′) in the non equilibrium case, which means they not only depend on the relative time but also the average time. The time evolution kernel becomes a Dyson Series. Answer TL;DR In general, no. A longer but possibly irrelevant discussion follows. … Read more