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  1. terra

    SU(2) lepton doublet conjugation rules

    I have a left-handed ##SU(2)## lepton doublet: ## \ell_L = \begin{pmatrix} \psi_{\nu,L} \\ \psi_{e,L} \end{pmatrix}. ## I want to know its transformation properties under conjugation and similar 'basic' transformations: ##\ell^{\dagger}_L, \bar{\ell}_L, \ell^c_L, \bar{\ell}^c_L## and the general...
  2. terra

    Lorentz transforming a momentum eigenstate

    Let's take a quantum state ##\Psi_p##, which is an eigenstate of momentum, i.e. ##\hat{P}^{\mu} \Psi_p = p^{\mu} \Psi_p##. Now, Weinberg states that if ##L(p')^{\mu}\,_{\nu}\, p^{\nu} = p'##, then ##\Psi_{p'} = N(p') U(L(p')) \Psi_{p}##, where ##N(p')## is a normalisation constant. How to...
  3. terra

    2j+1 d representation for Poincaré group

    I want to learn how to write down a particle state in some inertial coordinate frame starting from the state ##| j m \rangle ##, in which the particle is in a rest frame. I know how to rotate this state in the rest frame, but how does one write down a Lorentz boost for it? Note that I am not...
  4. terra

    Non-leptonic hadron decays: preferred paths?

    My background of some introductory courses in particle physics has left me with severe shortcomings. Say we start from a hadron, which decays purely to other hadrons. My question is this: through which interaction does the process take place? Is there a preferred interaction, and why/why not...
  5. terra

    Cohen-Tannoudji on mutually exclusive (?) events

    I was looking at what Cohen-Tannudji has to say on compatibility of observables. Assumptions: ## A,B## are operators such that ##[A,B]=0 ## and we denote ## |a_i \,b_j\rangle## to be states for which ##A | a_i \, b_j \rangle= a_i | a_i \, b_j \rangle##, ##B | a_i \, b_j \rangle= b_j | a_i \...
  6. terra

    Volume elements of phase space

    First, two definitions: let ## \varrho (M)## be the probability density of macro states ##M ## (which correspond to a subgroup of the phase space) and ## \mathrm{d} \Gamma ## be the volume element of a phase space. In my lecture notes, the derivation for continuity equation of probability...
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