scholarly journals On the Lorentz-Invariance of the Dyson Series in Theories with Derivative Couplings

2021 ◽  
Vol 66 (11) ◽  
pp. 945
Author(s):  
V. Denisi ◽  
A. Papa ◽  
M. Rossi
Keyword(s):  
Lorentz Invariance ◽  
Dyson Series ◽  
S Matrix ◽  
Feynman Rules ◽  
Derivatives Of ◽  
Wick’S Theorem

We study the Dyson series for the S-matrix, when the interaction depends on derivatives of the fields. We concentrate on two particular examples: the scalar electrodynamics and the renormalized ф4 theory. By using Wick’s theorem, we eventually give evidence that the Lorentz invariance is satisfied, and the usual Feynman rules can be applied to the interaction Lagrangian.

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.

scholarly journals Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

2017 ◽  
Vol 32 (27) ◽  
pp. 1750165 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Physical Model ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Point Of View ◽  
Inductive Method ◽  
S Matrix ◽  
Causal Approach

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

scholarly journals Feynman Rules for Magnetised Spin-O Bosons

1991 ◽  
Vol 44 (4) ◽  
pp. 335
Author(s):  
ET Rowe
Keyword(s):  
Vertex Function ◽  
Gordon Equation ◽  
Feynman Diagrams ◽  
New Class ◽  
Two Photon ◽  
S Matrix ◽  
Matrix Expansion ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Klein Gordon Equation

Solutions of the Klein-Gordon equation are given in the Landau and cylindrical gauges and these are used to calculate explicit forms of the vertex function. From an S-matrix expansion analogous to the spin-i case we obtain the Feynman rules for magnetised spin-O particles: the major differences between the spin-i and spin-O cases are the explicit forms of the respective vertex functions and the addition of a two-photon vertex in the spin-O case. This additional vertex makes possible a whole new class of Feynman diagrams.

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 A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY

2011 ◽  
Vol 08 (04) ◽  
pp. 821-834
Author(s):  
HOSSEIN GHORBANI ◽  
GIAMPIERO ESPOSITO
Keyword(s):  
Quantum Gravity ◽  
Gauge Invariance ◽  
Lorentz Invariance ◽  
Functional Integral ◽  
Coulomb Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
S Matrix ◽  
Ghost Field

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

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