By P. D. B. Collins
ISBN-10: 0471600881
ISBN-13: 9780471600886
This readable advent to particle physics and cosmology discusses the interplay of those primary branches of physics and considers contemporary advances past the traditional versions. 8 chapters contain a quick creation to the gauge theories of the robust and the electroweak interactions, the so-called grand unified theories, and normal relativity. Ten extra chapters handle fresh recommendations reminiscent of composite fermions and bosons, supersymmetry, quantum gravity, supergravity, and strings theories, and relate them to trendy cosmology and experimental astronomy.
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Example text
40). 39). 17). Thus, spatial components of Eq. 39) (μ = i = 1, 2, 3) read dui + Γi0j u0 uj + Γij0 uj u0 = 0, ds or dui a˙ dt i +2 u = 0. ds a ds In terms of the physical components the latter equation is a˙ dU i = − U i. 38) is indeed valid. Thus, the velocities of free particles with respect to comoving frame decrease in expanding Universe; particles gradually “freeze in”. In particular, if at early cosmological stages massive particles were relativistic, they become non-relativistic at later stages.
6) One of the properties of homogeneous and isotropic spaces is that all covariant geometrical quantities are expressed through the metric tensor γij and, possibly, tensors δij and Eijk , the latter existing in any Riemannian space, see Appendix A (here i, j = 1, 2, 3; we denote the metric tensor of 3-dimensional space by γij to distinguish it from the metric tensor gμν of 4-dimensional space-time). Furthermore, the coefficients do not depend on coordinates. 1. 7) that the Ricci tensor is κ (3) Rij = 2 2 γij , R and the curvature scalar is constant in space and equal to 6κR−2 .
In analogy to 3-sphere, 3-dimensional hyperboloid is conveniently described by its embedding into fictitious 4-dimensional Minkowski space with metric ds2 = −(dy 1 )2 + (dy 2 )2 + (dy 3 )2 + (dy 4 )2 , while the equation for the hyperboloid is (y 1 )2 − (y 2 )2 − (y 3 )2 − (y 4 )2 = R2 . 4) We are interested in the one connected component y 1 > 0. 1. Show that the hyperboloid is indeed a homogeneous and isotropic space. Hint: Begin with defining what precisely is a homogeneous and isotropic space.
Particle Physics and Cosmology by P. D. B. Collins
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