Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The rise of classical field theory
- Part I The geometrical programme for fundamental interactions
- Part II The quantum field programme for fundamental interactions
- 6 The rise of quantum theory
- 7 The formation of the conceptual foundations of quantum field theory
- 8 The quantum field programme (QFP)
- Part III The gauge field programme for fundamental interactions
- Appendices
- Bibliography
- Name index
- Subject index
8 - The quantum field programme (QFP)
Published online by Cambridge University Press: 21 January 2010
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 The rise of classical field theory
- Part I The geometrical programme for fundamental interactions
- Part II The quantum field programme for fundamental interactions
- 6 The rise of quantum theory
- 7 The formation of the conceptual foundations of quantum field theory
- 8 The quantum field programme (QFP)
- Part III The gauge field programme for fundamental interactions
- Appendices
- Bibliography
- Name index
- Subject index
Summary
The study of the interactions between electrically charged particles and electromagnetic fields within the framework of QFT is called quantum electrodynamics (QED). QED, and in particular its renormalized perturbative formulation, was modeled by various theories to describe other interactions, and thus became the starting point for a new research programme, the quantum field programme (QFP). The programme has been implemented by a series of theories, whose developments are strongly constrained by some of its characteristic features, which have been inherited from QED. For this reason, I shall start this review of the sinuous evolution of QFP with an outline of these features.
Essential features
QED is a theoretical system consisting of local field operators that obey equations of motion, certain canonical commutation and anticommutation relations (for bosons and fermions, respectively), and a Hilbert space of state vectors that is obtained by the successive application of the field operators to the vacuum state, which, as a Lorentz invariant state devoid of any physical properties, is assumed to be unique. Let us look in greater detail at three assumptions that underlie the system.
First is the locality assumption. According to Dirac (1948), ‘a local dynamical variable is a quantity which describes physical conditions at one point of space-time. Examples are field quantities and derivatives of field quantities,’ and “a dynamical system in quantum theory will be defined as localizable if a representation for the wave function can be set up in which all the dynamical variables are localizable’.
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- Information
- Conceptual Developments of 20th Century Field Theories , pp. 210 - 268Publisher: Cambridge University PressPrint publication year: 1997