scholarly journals The energy momentum spectrum and vacuum expectation values in quantum field theory, II

1971 ◽  
Vol 22 (1) ◽  
pp. 1-22 ◽  
Author(s):  
James Glimm ◽  
Arthur Jaffe
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Expectation ◽  
Momentum Spectrum ◽  
Quantum Field ◽  
Expectation Values

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 The energy-momentum spectrum in the Yukawa2 quantum field theory

1977 ◽  
Vol 57 (1) ◽  
pp. 31-50 ◽  
Author(s):  
Edward P. Heifets ◽  
Edward P. Osipov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Momentum Spectrum ◽  
Quantum Field

The energy-momentum operator in curved space-time

1983 ◽  
Vol 389 (1797) ◽  
pp. 379-403 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Momentum Operator ◽  
Quantum Field ◽  
Expectation Values ◽  
Curved Space ◽  
Renormalization Theory

We argue that the only meaningful geometrical measure of the energy—momentum of states of matter described by a free quantum field theory in a general curved space—time is that provided by a normal ordered energy-momentum operator. We contrast the finite expectation values of this operator with the conventional renormalized expectation values and further argue that the use of renormalization theory is inappropriate in this context.

Double refraction phenomena in quantum field theory

1958 ◽  
Vol 54 (1) ◽  
pp. 81-88 ◽  
Author(s):  
M. J. Stephen
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Optical Activity ◽  
Kerr Effect ◽  
Stokes Parameters ◽  
Quantum Field ◽  
Expectation Values ◽  
Scattering Problems ◽  
Double Refraction ◽  
Usual Quantum

ABSTRACTIt is shown that the phenomena of double refraction—optical activity, Faraday rotation, Kerr effect, etc.—may be treated as scattering problems in quantum field theory. An expression for the scattering cross-section of an atom or molecule for photons may be easily obtained and from this expression using the idea of Stokes operators, equating their expectation values to the classical Stokes parameters, the usual quantum mechanical expressions for optical activity, etc. may be obtained. This approach does not require the ideas of refractive index or polarization of the medium, and emphasizes what are the actual observables in these experiments.

The energy-momentum spectrum in theP(ϕ)2 quantum field theory

1977 ◽  
Vol 56 (2) ◽  
pp. 161-172 ◽  
Author(s):  
Edward P. Heifets ◽  
Edward P. Osipov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Momentum Spectrum ◽  
Quantum Field

scholarly journals QUANTUM FIELD THEORY IN CURVED SPACE–TIME, THE OPERATOR PRODUCT EXPANSION, AND DARK ENERGY

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2607-2615 ◽  
Author(s):  
STEFAN HOLLANDS ◽  
ROBERT M. WALD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Operator Product Expansion ◽  
Vacuum Expectation ◽  
Vacuum State ◽  
Space Time ◽  
Operator Product ◽  
Energy Tensor ◽  
Quantum Field ◽  
Curved Space

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved space–time, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved space–time does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a "vacuum state" and "particles". We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients — and, thus, the quantum field theory. By contrast, ground/vacuum states — in space–times, such as Minkowski space–time, where they may be defined — cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.

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