First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

This is a prize-winning study of an area of physics not previously explored by philosophy: gauge theory. Gauge theories have provided our most successful representations of the fundamental forces of nature. But how do such representations work? Healey defends an original answer to this question.

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. -/- This expanded edition features several additional chapters, as well as (...) an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading. (shrink)

Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the (...) wave function provides only a partial description of the system. This description is completed by the specification of the actual positions of the particles. The latter evolve according to the.. (shrink)

I distinguish three views, a defence of any one of which would go some way towards vindicating the view that there is something objective about the passage of time: the view that the present moment is objectively distinguished; the view that time has an objective direction – that it is an objective matter which of two non-simultaneous events is the earlier and which the later; the view that there is something objectively dynamic, flux-like, or "flow-like" about time. I argue that (...) each of these views is not so much false as doubtfully coherent. In each case, it turns out to be hard to make sense of what the view could be, at least if it is to be non-trivial, and of use to a friend of objective passage. I conclude with some remarks about avenues that seem worth exploring in the philosophy of time, when we are done with trying to make sense of passage. (shrink)

I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the ‘naive’ (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least (...) as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work. (shrink)

The Principle of Sufficient Reason is a powerful and controversial philosophical principle stipulating that everything must have a reason or cause. This simple demand for thoroughgoing intelligibility yields some of the boldest and most challenging theses in the history of metaphysics and epistemology. In this entry we begin with explaining the Principle, and then turn to the history of the debates around it. A section on recent discussions of the Principle will be added in the near future.

Like moths attracted to a bright light, philosophers are drawn to glitz. So in discussing the notions of ‘gauge’, ‘gauge freedom’, and ‘gauge theories’, they have tended to focus on examples such as Yang–Mills theories and on the mathematical apparatus of fibre bundles. But while Yang–Mills theories are crucial to modern elementary particle physics, they are only a special case of a much broader class of gauge theories. And while the fibre bundle apparatus turned out, in retrospect, to be the (...) right formalism to illuminate the structure of Yang–Mills theories, the strength of this apparatus is also its weakness: the fibre bundle formalism is very flexible and general, and, as such, fibre bundles can be seen lurking under, over, and around every bush. What is needed is an explanation of what the relevant bundle structure is and how it arises, especially for theories that are not initially formulated in fibre bundle language. Here I will describe an approach that grows out of the conviction that, at least for theories that can be written in Lagrangian/Hamiltonian form, gauge freedom arises precisely when there are Lagrangian/Hamiltonian constraints of an appropriate character. This conviction is shared, if only tacitly, by that segment of the physics community that works on constrained Hamiltonian systems. (shrink)

Ever since the now infamous comments made by Hermann Minkowski in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are equally real or whether the views espoused by the possibilists, historicists, and presentists regarding the unreality of the future (and, for presentists, the past) are best. Now, a century after Minkowski’s proposed blockworld first sparked debate, (...) we seek a more conclusive argument in favor of the eternalist picture of space-time. Utilizing an argument based on the relativity of simultaneity in the tradition of Putnam and Rietdijk and novel but reasonable assumptions as to the nature of “reality”, we will show that the past, present, and future are equally real, thus ruling out presentism and other theories of time that bestow special ontological status to the past, present, or future as untenable. Finally, we will respond to our critics who would suggest that: 1) there is no metaphysical difference between the positions of eternalism and presentism, 2) the present must be defined as the “here” as well as the “now”, or 3) presentism is correct and our understanding of relativity is incomplete because it does not incorporate a preferred frame. We call eternalist response 1 deflationary since it purports to dissolve or deconstruct the age-old debate between the two views and response 2 compatibilist because it does nothing to alter special relativity (SR) arguing instead that SR unadorned has the resources to save presentism. Response 3 we will call incompatibilism because it adorns SR in some way in order to save presentism a la some sort of preferred frame. We will show that neither move 1 nor 2 can save presentism and move 3 is not well motivated at this juncture except as an ad hoc device to refute eternalism. (shrink)

We articulate the problems posed by the quantum liar experiment (QLE) for backwards causation interpretations of quantum mechanics, time-symmetric accounts and other dynamically oriented local hidden variable theories. We show that such accounts cannot save locality in the case of QLE merely by giving up “lambda-independence.” In contrast, we show that QLE poses no problems for our acausal Relational Blockworld interpretation of quantum mechanics, which invokes instead adynamical global constraints to explain Einstein–Podolsky–Rosen (EPR) correlations and QLE. We make the case (...) that the acausal and adynamical perspective is more fundamental and that dynamical entities obeying dynamical laws are emergent features grounded therein. (shrink)

In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{0,1}$\end{document}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be (...) completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time. (shrink)

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the (...) so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity. (shrink)