Quantum Field Theory Beyond the S-Matrix Formalism

2020 ◽  
Vol 51 (4) ◽  
pp. 614-618
Author(s):  
I. P. Volobuev ◽  
V. O. Egorov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Formalism ◽  
Quantum Field ◽  
S Matrix

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 Black Hole Radiation, Greybody Factors, and Generalised Wick Rotation

2021 ◽  
Author(s):  
◽  
Finnian Gray
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Hawking Temperature ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Wick Rotation ◽  
Radiation Process ◽  
Black Hole Radiation ◽  
Euclidean Quantum Field Theory

<p>In this thesis we look at the intersection of quantum field theory and general relativity. We focus on Hawking radiation from black holes and its implications. This is done on two fronts. In the first we consider the greybody factors arising from a Schwarzschild black hole. We develop a new way to numerically calculate these greybody factors using the transfer matrix formalism and the product calculus. We use this technique to calculate some of the relevant physical quantities and consider their effect on the radiation process.  The second front considers a generalisation of Wick rotation. This is motivated by the success of Wick rotation and Euclidean quantum field theory techniques to calculate the Hawking temperature. We find that, while an analytic continuation of the coordinates is not well defined and highly coordinate dependent, a direct continuation of the Lorentzian signature metric to Euclidean signature has promising results. It reproduces the Hawking temperature and is coordinate independent. However for consistency, we propose a new action for the Euclidean theory which cannot be simply the Euclidean Einstein-Hilbert action.</p>

Quantum Field Theory

2020 ◽  
pp. 237-288
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Canonical Quantization ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coordinate Space ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

Perturbation Method for Boundary S-Matrix in 2D Quantum Field Theory

1997 ◽  
Vol 12 (38) ◽  
pp. 2951-2962 ◽  
Author(s):  
Nadia Topor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Free Parameter ◽  
Exact Expression ◽  
Quantum Field ◽  
Boundary Interaction ◽  
S Matrix ◽  
Sine Gordon Model ◽  
The One ◽  
Perturbative Result

We develop a perturbation theory for evaluating the boundary S-matrix in 2D quantum field theory. We apply this approach to calculate the one-loop boundary S-matrix for the elementary particle of the sine–Gordon model with a boundary interaction. Our perturbative result agrees with the exact expression of the S-matrix conjectured by Goshal; it also allows us to derive the perturbative relation between the parameter ϑ in the S-matrix and the free parameter M in the boundary action, in the particular case in which its other free parameter φ0 is zero.

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