Quantum field theory

1955 ◽  
Vol 231 (1186) ◽  
pp. 321-335 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Variational Principle ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
Functional Expression ◽  
Scattering Matrix ◽  
Classical Field ◽  
Quantum Field ◽  
Relativistic Analogue

A functional expression resembling the scattering matrix is introduced into classical field theory, and with this foundation a postulate of quantization is introduced analogous to the definitions of Feynmann. From this are derived some alternative and more familiar forms of field theory. A variational principle is introduced which provides a relativistic analogue of the familiar non-relativistie variational principle for the Schrödinger equation.

scholarly journals The relation between quantum and classical field theory with a classical source

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200656
Author(s):  
S. A. Fulling ◽  
A. G. S. Landulfo ◽  
G. E. A. Matsas
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Field Theory ◽  
Classical Field ◽  
Quantum Field ◽  
Schwarzschild Solution ◽  
Classical Source ◽  
Time Quantum ◽  
Perturbative Quantum ◽  
Classical Picture

Classical field theory is about fields and how they behave in space–time. Quantum field theory, in practice, usually seems to be about particles and how they scatter. Nevertheless, classical fields must emerge from quantum field theory in appropriate limits, and Michael Duff showed how this happens for the Schwarzschild solution in perturbative quantum gravity. In a series of papers, we and others have shown how classical radiation from an accelerated charge emerges from quantum field theory when the Unruh thermal effect is taken into account. Here, we sharpen those conclusions by showing that, even at finite times, the quantum picture is meaningful and is in close agreement with the classical picture.

From Classical to Quantum Fields

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Laws Of Nature ◽  
Classical Field Theory ◽  
Functional Integral ◽  
Theoretical Physics ◽  
Standard Theory ◽  
Quantum Field ◽  
Detailed Model ◽  
Universal Language

Quantum field theory has become the universal language of most modern theoretical physics. This book is meant to provide an introduction to this subject with particular emphasis on the physics of the fundamental interactions and elementary particles. It is addressed to advanced undergraduate, or beginning graduate, students, who have majored in physics or mathematics. The ambition is to show how these two disciplines, through their mutual interactions over the past hundred years, have enriched themselves and have both shaped our understanding of the fundamental laws of nature. The subject of this book, the transition from a classical field theory to the corresponding Quantum Field Theory through the use of Feynman’s functional integral, perfectly exemplifies this connection. It is shown how some fundamental physical principles, such as relativistic invariance, locality of the interactions, causality and positivity of the energy, form the basic elements of a modern physical theory. The standard theory of the fundamental forces is a perfect example of this connection. Based on some abstract concepts, such as group theory, gauge symmetries, and differential geometry, it provides for a detailed model whose agreement with experiment has been spectacular. The book starts with a brief description of the field theory axioms and explains the principles of gauge invariance and spontaneous symmetry breaking. It develops the techniques of perturbation theory and renormalisation with some specific examples. The last Chapters contain a presentation of the standard model and its experimental successes, as well as the attempts to go beyond with a discussion of grand unified theories and supersymmetry.

STOCHASTIC QUANTIZATION OF THE KINK SOLUTION OF ϕ4 FIELD THEORY

1989 ◽  
Vol 04 (01) ◽  
pp. 39-46
Author(s):  
RONALD KATES ◽  
ARNOLD ROSENBLUM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Classical Field ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Field Equations ◽  
Kink Solution

The method of Parisi-Wu Stochastic quantization in quantum field theory is compared to earlier work in classical field equations. The method is applied to solve for the propagator of ϕ4 field theory by perturbing the Kink solution.

Sign in / Sign up

Export Citation Format

Share Document