By Walter Greiner
Gauge thought of vulnerable Interactions treats the unification of electromagnetic and susceptible interactions and considers comparable phenomena. First, the Fermi conception of beta decay is gifted, via a dialogue of parity violation, clarifying the significance of symmetries. Then the concept that of a spontaneously damaged gauge concept is brought, and all important mathematical instruments are conscientiously constructed. The "standard version" of unified electroweak interactions is punctiliously mentioned together with present advancements. the ultimate bankruptcy comprises an creation to unified theories of sturdy and electroweak interactions. quite a few solved examples and difficulties make this quantity uniquely perfect as a textual content for a complicated direction. This fourth version has been rigorously revised.
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Extra resources for Gauge Theory of Weak Interactions
44) 37 38 2 Leptonic Interactions which implies that q μ = k μ + k ′ μ cannot be satisfied. Therefore for q 2 < 0 . 46b) . 47b) yielding the solution π Θ(q 0 )Θ(q 2 ) , 24 π B = Θ(q 0 )Θ(q 2 ) . 49) . 50) . 50). For a moving muon we have p ′0 = γ mμ with the Lorentz factor γ = (1 − v 2 /c2 )−1/2 . 50), dW ∝ 1/γ , implying that the decay rate decreases considerably for fast-moving muons, that is, the life-time τμ ∝ γ is prolonged. To proceed we switch to the rest frame of the muon, which is characterized by p α ′ − p α = (mμ − p 0 , −p).
2. Configuration for which the electron reaches its maximum value of momentum 0 0 + k 0 + k ′0 = pmax + |k| + |k ′ | mμ = pmax 0 = pmax + |p max | 0 0 = pmax + (pmax )2 − m2e 1 2 . 53). 55) . 55) we used the fact that the averaging over s gives s = 0 so that also s 0 = m1 p · s = 0 (cf. 23)). 57) with the abbreviation y ≡ m2e /m2μ . 87 × 10−4 ) . 57) it is obvious that the decay rate would vanish if y = 1. This reflects the fact that in this (academic) case the muon would be stable since |p max | = 0, so that there would be no phase space available for the final-state electron.
22) αβ See W. Greiner and J. Reinhardt: Quantum Electrodynamics, 4th ed. (Springer, Berlin, Heidelberg, 2009). 23) , where s ′ is the spin vector with respect to the rest frame. Here s ′ is a unit vector so that s ′μ sμ′ = −1. 20) we obtain the following expression for the muonic contribution to the transition currents Xμν (μ): X μν (μ) = t′ 1 + γ5 /s′ 2 μ (1 − γ5 )̺α (/ u¯ νμ (k ′ , t ′ )π γπ̺ p ′ + mμ ) αβ ν (1 − γ5 )σ τ uνμ (k ′ , t ′ )τ × γβσ μ (1 − γ5 )̺α (/ = γπ̺ p ′ + mμ ) 1 + γ5 /s′ 2 αβ ν (1 − γ5 )σ τ k/′τ π γβσ .