Over the past decades a remarkable evolution has occurred in the development of particle physics in relation to general relativity, astrophysics, and cosmology. Till the early 1960s, gravity was considered a force not strong enough to be a player along with the electroweak and the strong forces, and did not receive any significant attention in texts on particle theory till that time. However, these perceptions changed at a remarkably rapid pace in the second half of the last century, most directly due to the discovery of supersymmetry and supergravity and, later, string theory. Thus, supergravity theory and theories based on superstrings bring gravity into the mix in an intrinsic fashion. Models based on supergravity, specifically supergravity grand unification, indicate that electroweak phenomena are driven by supergravity-induced effects connecting in a remarkable way the Planck scale with the electroweak scale. Another way that the connection between particle physics and cosmology has deepened over the past decades is due to the experimental observations that the universe is composed mostly of dark matter and dark energy, and particle theory is the likely place to achieve an understanding of these phenomena. Thus, while dark energy could be sourced by a tiny cosmological term in the Einstein equations, models based on supersymmetry and supergravity provide dark matter candidates in the form of a neutral spin 1/2 particle (the neutralino) and a spin 3/2 particle (the gravitino). Further, the early history of the universe is driven by particle physics via phenomena such as baryogenesis and leptogenesis, which can provide the observed baryon excess in the universe. Thus, currently there exists an unprecedented degree of fusion of astrophysics, cosmology, and particle theory. Each of these disciplines has its own glorious history with texts that center on them. However, for a young researcher entering the field of particle theory, developing a workable knowledge of these diverse fields presents a challenge. This text is written with the hope that it may make that task a bit easier. The text is written with the assumption that the reader has a workable knowledge of field theory.

Since the underlying theme of the book is unification, a number of interconnected topics are discussed. These include Einstein and Yang–Mills theories, the standard model, supersymmetry and supergravity, and cosmology along with some specialized topics.

Physical Constants

Speed of light in vacuum: c = 299 792 458 ms −1

Gravitational constant: GN = 6. 67428(67) × 10 −11 m3 kg −1s−2

= 6. 70881(67) × 10 −39 ħc (GeVc−2) −2

Planck's constant: h = 6. 62606896(33) × 10 −34 J s

(Planck's constant)/2π: ħ = 1. 054571628(53) × 10 −34 J s

= 6. 58211899(16) × 10 −22 MeV s

Reduced Planck mass: MPl = (8πGN/ħc) −1/2

= 2. 43 × 1018GeVc2

Fine structure constant: α = e2/ħc = 1/137. 035

Fermi constant: GF/(ħc)3 = 1. 16637(1) × 10 −5 GeV −2

Boltzmann constant: kB = 1. 3806504(24) × 10 −23 JK −1

= 8. 617343(15) × 10 −5 eVK −1

Electron mass: me = 0. 51099 MeV

Proton mass: mp = 938. 2720 MeV

W−boson mass: MW = (80. 399 ± 0. 023) GeV

Z − boson mass: MZ = (91. 1876 ± 0. 0021) GeV

Strong coupling constant: αs (MZ) = 0. 1184(7)

Electron electric dipole moment: de < (7 ± 7) × 10 −28 ecm

Neutron electric dipole moment: dn < 0. 29 × 10 −25 ecm,

confidence limit (CL) = 90%

Some useful conversions are

The values of the physical constants listed are from K. A. Olive et al. (Particle Data Group), “Review of Particle Physics,” Chin. Phys. C 38, 090001 (2014).

Natural Units

Often, it is convenient to use units where the natural physical constants assume unit values. For instance, if we assume units so that

then in these units energy can be expressed as inverse length since L = ħc/E = 1/E, which gives

One may also assume as fundamental units the Boltzmann constant and Newton's constant so that

Equations (23.1) and (23.2) taken together are often referred to as Planck natural units.

Baryon number in particle theory has been of interest for several decades. In 1929 Herman Weyl [1] conjectured such a conservation, and later in 1938 Stueckelberg [2] made it more concrete. This was done by postulating different transformation laws for light particles and heavy particles where the leptons were the light and the nucleons the heavy particles. The conservation of baryons was put on an equal footing to the conservation of the electric charge in further work by Wigner [3]. On the experimental side, the earliest work on putting a lower limit on the proton lifetime was by Goldhaber [4]. In 1954 Goldhaber proposed that spontaneous fission of Th232 after excitation by nucleon decay would be followed by a rearrangement energy due to the loss of a nucleon, and this would cause fission of the residual nucleus. This allowed Goldhaber to put a lower limit of 1.4 × 1014 years on the nucleon lifetime. This limit was soon improved to a lower limit of 1 × 1022 years for bound nucleons in a direct experiment using a liquid scintillation counter 30 m below the Earth's surface by Reines, Cowan, and Goldhaber [5] (for a review of the early history of experiment on proton lifetime limits see Gurr et al. [6] and Perkins [7], and for a broad overview of proton stability in grand unified theories, strings, and branes see Nath and Fileviez Perez [8]). On the theoretical side, an issue arose regarding the absolute conservation of baryon number. It was pointed out by Lee and Yang [9] that if heavy particle number is the result of a gauge invariance, there would be a longrange force associated with such a conservation, but no such long range force is observed. On the other hand, if baryon number is a global symmetry, there is no reason that a global symmetry would guarantee an absolute conservation of baryon number. Indeed, such a symmetry would be violated by anomalies [10] and by gravitational interactions [11–14], specifically worm hole effects [15]. The first concrete model for proton decay via a possible new superweak interaction was discussed by Yamaguchi in 1959 [16]. This work stimulated the first deep underground proton decay experiment in 1960 [7, 17].