vol 2: Synopsis
part III: Modern physics
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Quantum field theory
Quantum mechanics, like Newtonian mechanics, provides a general paradigm for the study of motion. Newtonian mechanics struck trouble when it came to deal with electromagnetism. This problem ultimately led to the development of quantum theory. Quantum theory, in its turn, revealed itself to be very difficult to harmonize with Einstein's special theory of relativity. Quantum field theory has evolved to deal with this difficulty and provides us with a wide ranging picture of the universe called the standard model.
The essential content of the special theory of relativity is that the laws of physics are the same in all inertial frames of reference. What changes is how things in one frame of reference look when viewed from another frame of reference in relative motion. This change affect not only human observers. It is a constitutive feature of the universe, arising from the finite velocity of communication between different points in the universe. It seems that all things 'observe' and 'act' upon one another as though special relativity were true for them.
We move from one frame of reference to another via a Lorentz transformation. A Lorentz transformation can be understood as a rotation in four dimensional spacetime. The actual structure of the Lorentz transformation is based on the axiom that the velocity of light is the same for all observers. Communication carries us from one frame of reference to another.
To simplify the problem of gravitation, Newton assumed instantaneous action at a distance. Not only does modern physics hold that no action is instantaneous, it also holds that proximity is necessary for interaction. All communication in the universe is mediated by particles moving from one point to another. Conceptually, particles are a localized entity. We understand the movement (including the creation and annihilation) of particles to be controlled by fields, that is structures that exist throughout spacetime.
One consequence of the structure of spacetime revealed by the special theory is that there is an equivalence between mass and energy. Energy may be created out of massive particles, and massive particles may be created out of energy. Quantum field theory describes this process of the creation and annihilation of particles, telling us how frequently it will happen and what can be created from the annihilation of what.
There are four fields, called gravitation, electromagnetic, strong and weak. Gravitation is responsible for the overall structure of the universe described by the general theory of relativity. The electromagnetic field, carried by the photon, and its interactions with electrically charged matter, is described by quantum electrodynamics. Both gravitation and electromagnetic fields have unlimited range, and so can be sensed at the macroscopic level. We are all familiar with the pull of gravity which keeps us on the earth, and have played with magnets, so feeling the electromagnetic field.
The other two fields, strong and weak, have extremely short range, but are nevertheless essential to the functioning of the universe. Quantum field theory shows how the particles of the universe form a complete set, spanning all possible communications of all possible information.
Books
| Greene, Brian, The Elegant Universe: superstrings, hidden dimensions and the quest for the ultimate theory, W W Norton and Company 1999 Jacket: 'Brian Greene has come forth with a beautifully crafted account of string theory - a theory that appears to be a most promising way station to an ultimate theory of everything. His book gives a clear, simple, yet masterful account that makes a complex theory very accessible to nonscientists but is also a delightful read for the professional.' David M Lee Amazon back |
| Nakahara, Mikio, Geometry, Topology and Physics, Adam Hilger 1990 Jacket: 'Differential geometry and topology have become essential tools for many theoretical physicists. [this book] introduces the ideas of differential geometry and topology to postgraduate students and researchers of theoretical physics. ... Throughout the book there are explicit calculations and diagrams to clarify the abstract ideas involved. A large number of problems and exercises are included to help develop the reader's understanding of the subject.' Amazon back |
| Pais, Abraham, Inward Bound: Of Matter and Forces in the Physical World, Clarendon Press, Oxford University Press 1986 Preface: 'I will attempt to describe what has been discovered and understood about the constituents of matter, the laws to which they are subject and the forces that act on them [in the period 1895-1983]. ... I will attempt to convey that these have been times of progress and stagnation, of order and chaos, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big moneys.' AP Amazon back |
| Siegel, Warren, Introduction to String Field Theory, World Scientific 1988 Introduction: 'The experiments that gave us quantum theory and general relativity are now quite old, but a satisfactory theory which is consistent with both of them has yet to be found. ... Strings ... offer a possibility of consistently describing all of nature. However, even if strings eventually turn out to disagree with nature, or to be too intractable to be useful for phenomenological applications, they are still the only consistent toy models of quantum gravity ... so their study willbe useful for discovering new properties of quantum gravity.' page 1. Amazon back |
| Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...' Amazon back |
| Weinberg, Steven, The Quantum Theory of Fields Volume II: Modern Applications, Cambridge University Press 1996 Jacket: '[This volume] gives an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problemd of elemntary partricle physics and condensed matter physics to which they have been applied. Topics are incl;uded that are not usually found in books on quantum field theory, such as the Batalin-Vilkovsky formalism and its application to renomralisation and anomalies in gauge theories; the background field method; the effective field theory approach to symmetry breaking; critical phenomena; and superconductivity. The book contains original material and is peppered with examples and insights from the author's experience as a lkeader of elementary particle physics. Problems are inlcuided at the end of each chapter.' Amazon back |
| Weinberg, Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' Amazon back |
| Weinberg, Steven, The Quantum Theory of Fields, Volume III:, Cambridge University Press 2000 Jacket: '[This volume] presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics that is likely to be the centre of future progress in the physics of elementary particles and gravitation. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, super-graphs, non-perturbative results, theories of supersymmetry in high dimensions, and supergravity. A thorough review is given of the phenomenological implications of sypersymmetry, including theories of both gauge and gravitationally mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. The book contains much material not found in other books on supersymmetry, some of it new. Problems are included at the end of each chapter.' Amazon back |
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