Physical Foundations of Cosmology

140 The very early universe This color combination would only occur if the unit matrix were among theλ matrices. But the unit ma ...

4.2 Quantum chromodynamics and quark–gluon plasma 141 Problem 4.5Verify that color–anticolor and three-quark combinations are re ...

142 The very early universe pμ qμ 1 p μ 2 Fig. 4.3. The diagrams containing closed loops are generically divergent. Fortunately, ...

4.2 Quantum chromodynamics and quark–gluon plasma 143 figure out the structure of perturbative expansion (4.22) and find a way t ...

144 The very early universe the expression on the right hand side of these equations, β(α)=f 1 ′( 1 )α^2 +f 2 ′( 1 )α^3 +···, (4 ...

4.2 Quantum chromodynamics and quark–gluon plasma 145 Fig. 4.4. diagrams with virtualgluonbubbles (Figure 4.4). Their contributi ...

146 The very early universe quantum chromodynamics is known asasymptotic freedom. The decrease in the coupling constant is due t ...

4.2 Quantum chromodynamics and quark–gluon plasma 147 but atTQCDthey constitute only a small fraction of the total energy dens ...

148 The very early universe Whether the transition from the quark–gluon plasma to hadronic matter is char- acterized by truly si ...

4.2 Quantum chromodynamics and quark–gluon plasma 149 the pressure should be continuous, allowing both phases (hadrons and quark ...

150 The very early universe for instance, the formation of quark nuggets, the generation of magnetic fields and gravitational wa ...

4.3 Electroweak theory 151 gauge symmetry. The gauge coupling constants of theSU( 2 )andU( 1 )groups should be taken as independ ...

152 The very early universe described by four component spinors with the first two components equal to zero. To make concrete ca ...

4.3 Electroweak theory 153 andU( 1 )transformations, ψL→e−ig ′YLλ(x) ψL,ψR→e−ig ′YRλ(x) ψR, if the gauge fieldsAμandBμtransform ...

154 The very early universe gauge-invariant form, it will remain renormalizable. This is what really happens in spite of the fac ...

4.3 Electroweak theory 155 written as φ=χ ( ζ 1 ζ 2 ) =χ ( ζ 2 ∗ ζ 1 −ζ 1 ∗ ζ 2 )( 0 1 ) ≡χζφ 0 , (4.47) whereχis a real field a ...

156 The very early universe The fieldsBμandGμchange underU( 1 )transformations. FieldBμtransforms as Bμ→Bμ+∂μλ. (4.54) Taking in ...

4.3 Electroweak theory 157 where Fμν(A)≡∂μAν−∂νAμ+igsinθw ( Wμ−Wν+−Wν−Wμ+ ) , Fμν(Z)≡∂μZν−∂νZμ+igcosθw ( Wμ−Wν+−Wν−Wμ+ ) , (4.62 ...

158 The very early universe fine structure constant” αw≡ g^2 4 π = e^2 4 πsin^2 θw (4.69) is in fact larger thanα≡e^2 / 4 π 1 / ...

4.3 Electroweak theory 159 Alternatively, using definitions (4.56), (4.57) and (4.71), we obtain Lf= i ( e ̄γμ∂μe+ν ̄Lγμ∂μνL ) − ...