We close with a brief introduction to Galois theory and illustrate the application of these mathematical ideas in physics through examples from conformal field theory.

This chapter contains introductory material, including visual examples that motivate the rest of the book. It explains the book formatting, previews the notation, provides pointers for getting started with Julia, and briefly reviews fields and vector spaces.

This chapter explains what we mean by “fields” and “waves” in physics, and argues that quantum waves are just as “real” as other waves we experience in daily life, such as water waves and sound waves.

The Conclusion recapitulates the ways in which the shifting balance of scientific opinion, economic power and bureaucratic intervention (which was inevitably political) shaped the trajectory of wine over the course of the twentieth century and into the new millennium. The lesson is that innovations in one field did not necessarily spill over into the others, which often meant that they stalled. Race runs as a thread through this history because its inscription in laws shaped consumption patterns, had a bearing on export possibilities, and led producers and merchants alike to set their priorities according to their reading of the market and where the profits lay. The Conclusion ends by speculating about whether the legacies of racial framings are finally being addressed.

The purpose of this chapter is to clearly define the mathematical objects that describe particles of various kinds: bosons (spin-0 and spin-1) or spin-1/2 fermions. Starting from the Schrödinger equation, the Klein–Gordon equation, the Dirac equation and the Maxwell equations are detailed, leading to the description of the associated quantised field – a well-adapted framework to treat states composed of many particles that can be created or annihilated when they interact. The notion of 4-current is introduced, and the quantisation of the various fields is presented. With the Dirac equation, the spinor’s properties are described extensively. The interpretation of the solutions of the Dirac equation in terms of antiparticles and spin or helicity degrees of freedom is then detailed. Helicity and chirality are also treated carefully. Finally, the Maxwell field and the Proca field are described, highlighting their specificities in terms of polarisation degrees of freedom.

A quick introduction to the standard model of particle physics is given. The general concepts of elementary particles, interactions and fields are outlined. The experimental side of particle physics is also briefly discussed: how elementary particles are produced with accelerators or from cosmic rays and how to observe them with detectors via the interactions of particles with matter. The various detector technologies leading to particle identification are briefly presented. The way in which the data collected by the sensors is analysed is also presented: the most frequent probability density functions encountered in particle physics are outlined. How measurements can be used to estimate a quantity from some data and the question of the best estimate of that quantity and its uncertainty are explained. As measurements can also be used to test a hypothesis based on a particular model, the hypothesis testing procedure is explained.

A very short and simple introduction to continuous and discontinuous fields and some related quantities.

Rejecting the notion, endorsed by John Searle, of an “individual institution,” this chapter treats them as inherently social, and expresses no surprise that institutions have formed a central focus of sociological analysis since the discipline's founding. Engaging especially with work in the area of organizational theory and, beyond sociology, organizational and management studies, this chapter identifies an underlying dimension along which the literature can be arrayed, running from (macro, structural) scripts to (more micro, agentic) skills, as embodied in work by John Meyer and Neil Fligstein, respectively. Between these endpoints, this chapter identifies not only a similarly well-known Scandinavian institutionalism associated with March and Olsen and focusing on the microfoundation of bounded rationality, but also literature on institutional logics and institutional work emerging from business and management programs and only now starting to impact the broader social sciences. Beyond traditional strengths in explaining institutional maintenance, work in these idioms is making real progress in accounting for institutional origins and change.

This chapter transitions from the foundational topics of the previoustwo chapters, to more “working” mathematics. Thischapter builds up intuitions about some simple algebraic concepts– groups, rings, and fields. Some diagrams of“inconsistent vectors” are played with. The discussionis organized around how to deal with an open problem in inconsistentmathematics from Dunn and Mortensen, of how to allow some nontrivialinconsistency in fields. The idea of using relative unit elements ingroup cancellation – more than one “zero”number – is introduced as a possible solution, and its basicrules are developed.

While gravity was the first of the fundamental forces to be quantified and at least partially understood -- beginning all the way back in the seventeenth century -- it took an additional 200 years for physicists to unravel the secrets of a second fundamental force, the electromagnetic force. Ironically, it is the electromagnetic force that is by far the stronger of the two, and at least as prevalent in our daily lives. The fact that atoms and molecules stick together to form the matter we are made of, the contact forces we feel when we touch objects around us, and virtually all modern technological advances of the twentieth century, all these rely on the electromagnetic force. In this chapter, we introduce the subject within the Lagrangian formalism and demonstrate some familiar as well as unfamiliar aspects of this fascinating fundamental force of Nature.

This chapter connects analyses of transnational legal orders with research in field sociology and cultural sociological work on performance and power. Research on transnational legal orders opens up the opportunity to study processes of legal change that focus on status enhancement, networks, and peer review, in addition to more formal processes of legal regulation, enforcement, and compliance. We do so by focusing on human rights recommendations regarding rape and sexual violence, within the context of the UN’s Universal Periodic Review (UPR). The UPR process is uniquely suited to studying global norms, since the materials reviewed include national state reports, civil society reports, and a compiled report from international institutions – and within a peer review framework, states then respond by either accepting or merely noting the recommendations they receive. Through multiple correspondence analysis, we geometrically map out distinct groups of states involved in the process, and using a series of growth curve models, we show that recommendation acceptance is partially driven by particular types of states interacting within the UPR. In so doing, we develop connecting points between research on transnational legal orders, field sociology, and cultural sociology in order to better understand the performance of human rights.

We here make some suggestions as to how a specifically sociological approach to politics can build upon the course corrections recently made in political and historical sociology, as well as in the theory of action and of social structures. We argue that late-twentieth-century political sociology was led in several directions that were unprofitable. First, this political sociology was characterized by a disproportionate (and largely disappointing) focus on large-scale transitions, like revolutions, or other significant outcomes, at the expense of the examination of regularities in conventional political process. Second, the sociology that did treat everyday, lay, political behavior tended to embrace a notion of action that confused the reasons people gave for their choices with the predictors of their actions. Third, there was relatively little attention to the sociology of political elites as members of face-to-face groups with their own imperatives and organizational principles.

For the last half century, theory in political sociology has been dominated at different times by materialist or idealist approaches. From the mid-1960s to the mid-1980s, political economy and conflict theories seemed to prevail, led by Marxist theories but followed by other forms of conflict theories, such as resource mobilization and power resources theory. At this time, political economy approaches tried to bend culture into the class conflict process (see item 1 in Figure 8.1 with the dark circle representing political economy). For instance, gender and race issues were often filtered through class conflict lenses.