*Anthony Duncan*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199573264
- eISBN:
- 9780191743313
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573264.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the perturbative aspects of interacting field theory: namely, the techniques appropriate for studying those aspects of local quantum field theories which emerge from a formal ...
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This chapter discusses the perturbative aspects of interacting field theory: namely, the techniques appropriate for studying those aspects of local quantum field theories which emerge from a formal asymptotic expansion in some parameter of the theory, both from an operatorial as well as a path-integral point of view. Perturbative expansions are shown to have a natural interpretation in terms of graphical objects (Feynman graphs), with simple rules (Feynman rules) allowing the evaluation of the amplitudes in terms of elementary algebraic expressions associated with each graphical element (line, vertex, etc.). This is done first using operatorial methods: the matrix elements of Heisenberg picture operators needed for the LSZ formula are expanded using the Gell–Mann–Low theorem, and the resultant expressions evaluated using Wick's theorem. The resultant graphical objects arise naturally in a path-integral formulation of the field theory. Finally, the significance of Haag's theorem is discussed to demonstrate the validity of results obtained in perturbation theory via interaction-picture methods.Less

This chapter discusses the perturbative aspects of interacting field theory: namely, the techniques appropriate for studying those aspects of local quantum field theories which emerge from a formal asymptotic expansion in some parameter of the theory, both from an operatorial as well as a path-integral point of view. Perturbative expansions are shown to have a natural interpretation in terms of graphical objects (Feynman graphs), with simple rules (Feynman rules) allowing the evaluation of the amplitudes in terms of elementary algebraic expressions associated with each graphical element (line, vertex, etc.). This is done first using operatorial methods: the matrix elements of Heisenberg picture operators needed for the LSZ formula are expanded using the Gell–Mann–Low theorem, and the resultant expressions evaluated using Wick's theorem. The resultant graphical objects arise naturally in a path-integral formulation of the field theory. Finally, the significance of Haag's theorem is discussed to demonstrate the validity of results obtained in perturbation theory via interaction-picture methods.

*Laura Ruetsche*

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199535408
- eISBN:
- 9780191728525
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199535408.003.0011
- Subject:
- Philosophy, Philosophy of Science

This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and ...
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This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and explanations (such as the appeal to cosmological particle creation to account for decelerating cosmic expansion) best understood in terms of particles. Looking close at these techniques and explanations, the chapter argues that they rely on the presence of unitarily inequivalent representations, the very presence, Chapters 8 and 9 contended, that frustrates fundamental particle interpretation.Less

This chapter considers another route to a particle interpretation of quantum field theory, one mediated by the existence of techniques (such as the use of Feynman diagrams to guide calculation) and explanations (such as the appeal to cosmological particle creation to account for decelerating cosmic expansion) best understood in terms of particles. Looking close at these techniques and explanations, the chapter argues that they rely on the presence of unitarily inequivalent representations, the very presence, Chapters 8 and 9 contended, that frustrates fundamental particle interpretation.

*Michael Silberstein, W.M. Stuckey, and Timothy McDevitt*

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198807087
- eISBN:
- 9780191844850
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198807087.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, History of Physics

A brief introduction to particle physics and quantum field theory (QFT) is presented in the main thread of chapter 5. The impasse of unification in particle physics is historically reviewed, showing ...
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A brief introduction to particle physics and quantum field theory (QFT) is presented in the main thread of chapter 5. The impasse of unification in particle physics is historically reviewed, showing that the dynamical paradigm pervades the development of particle physics and QFT. Thus, as with the conundrums of general relativity and quantum mechanics, dynamical explanation in the mechanical universe is responsible for the impasse regarding unification in particle physics as per QFT. It is shown that RBW’s adynamical approach provides an entirely new view of unification and particle physics. Philosophy of Physics for Chapter 5 uses RBW to resolve the interpretational issues of gauge invariance, gauge fixing, the Aharonov–Bohm effect, regularization, and renormalization, and largely discharges the problems of Poincaré invariance in a graphical approach, inequivalent representations, and Haag’s theorem. Foundational Physics for Chapter 5 shows how classical field theory is related to QFT and introduces gauge fields per QFT.Less

A brief introduction to particle physics and quantum field theory (QFT) is presented in the main thread of chapter 5. The impasse of unification in particle physics is historically reviewed, showing that the dynamical paradigm pervades the development of particle physics and QFT. Thus, as with the conundrums of general relativity and quantum mechanics, dynamical explanation in the mechanical universe is responsible for the impasse regarding unification in particle physics as per QFT. It is shown that RBW’s adynamical approach provides an entirely new view of unification and particle physics. Philosophy of Physics for Chapter 5 uses RBW to resolve the interpretational issues of gauge invariance, gauge fixing, the Aharonov–Bohm effect, regularization, and renormalization, and largely discharges the problems of Poincaré invariance in a graphical approach, inequivalent representations, and Haag’s theorem. Foundational Physics for Chapter 5 shows how classical field theory is related to QFT and introduces gauge fields per QFT.