Dynamical derivation of the Yang–Mills S-matrix

1982 ◽  
Vol 60 (11) ◽  
pp. 1630-1640
Author(s):  
Robert E. Pugh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Equation ◽  
Quantum Field ◽  
Yang Mills ◽  
Covariant Quantum ◽  
S Matrix ◽  
Feynman Rules

The Feynman rules for self-interacting Yang–Mills fields are derived within the framework of conventional covariant quantum field theory by explicitly calculating the contributions of the nonphysical field components to the violations of the S-matrix equation of continuity.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

Interacting Fields

2021 ◽  
pp. 237-252
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Feynman Rules ◽  
Wightman Axioms

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

scholarly journals Galilean covariance, Casimir effect and Stefan–Boltzmann law at finite temperature

2017 ◽  
Vol 32 (16) ◽  
pp. 1750094 ◽  
Author(s):  
S. C. Ulhoa ◽  
A. F. Santos ◽  
Faqir C. Khanna
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Temperature ◽  
Temperature Effects ◽  
Casimir Effect ◽  
Quantum Field ◽  
Covariant Quantum ◽  
Thermo Field Dynamics ◽  
Boltzmann Law ◽  
Galilean Covariance

The Galilean covariance, formulated in 5-dimensions space, describes the nonrelativistic physics in a way similar to a Lorentz covariant quantum field theory being considered for relativistic physics. Using a nonrelativistic approach the Stefan–Boltzmann law and the Casimir effect at finite temperature for a particle with spin zero and 1/2 are calculated. The thermo field dynamics is used to include the finite temperature effects.

scholarly journals DIFFERENTIAL GEOMETRY FROM QUANTUM FIELD THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350003
Author(s):  
W. F. CHEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Geometry ◽  
Historical Development ◽  
Theoretical Physics ◽  
Quantum Field ◽  
Yang Mills ◽  
And Mathematics

We review the historical development and physical ideas of topological Yang–Mills theory and explain how quantum field theory, a physical framework describing subatomic physics, can be used as a tool to study differential geometry. We further emphasize that this phenomenon demonstrates that the inter-relation between theoretical physics and mathematics have come into a new stage.

scholarly journals Locally covariant quantum field theory and the spin–statistics connection

2016 ◽  
Vol 25 (06) ◽  
pp. 1630015 ◽  
Author(s):  
Christopher J. Fewster
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Axiomatic Approach ◽  
Quantum Field ◽  
General Version ◽  
Curved Spacetime ◽  
New Approach ◽  
Covariant Quantum ◽  
Specific Focus ◽  
Spin And Statistics

The framework of locally covariant quantum field theory (QFT), an axiomatic approach to QFT in curved spacetime (CST), is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin–statistics connection in CSTs than previously available. This part of the text is based on [C. J. Fewster, arXiv:1503.05797.] and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.

scholarly journals Classical simulation of quantum fields I

2006 ◽  
Vol 84 (10) ◽  
pp. 861-877 ◽  
Author(s):  
T Hirayama ◽  
B Holdom
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Zero Point ◽  
Background Field ◽  
Field Configuration ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Point Energy ◽  
Classical Simulation ◽  
Feynman Rules

We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler–Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In [Formula: see text] theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk

scholarly journals Broken Symmetry and Yang–Mills Theory

2014 ◽  
Vol 03 (01) ◽  
pp. 54-67 ◽  
Author(s):  
François Englert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Yang Mills

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang–Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues.

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