scholarly journals Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Cédric Lorcé ◽  
Andreas Metz ◽  
Barbara Pasquini ◽  
Simone Rodini
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Nucleon Mass ◽  
Quantum Field ◽  
Mechanical Equilibrium ◽  
Minimal Subtraction ◽  
Sum Rule ◽  
Trace Anomaly ◽  
Recent Developments ◽  
Translation Symmetry

Abstract We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincaré symmetry. We also study the concept of “quantum anomalous energy” proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.

scholarly journals THE LOCALLY COVARIANT DIRAC FIELD

2010 ◽  
Vol 22 (04) ◽  
pp. 381-430 ◽  
Author(s):  
KO SANDERS
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Covariant Quantum ◽  
Dimensional Spacetime ◽  
Stress Energy ◽  
Hadamard States ◽  
Stress Energy Momentum Tensor

We describe the free Dirac field in a four-dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra, the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally, we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.

scholarly journals CLASSICAL TRACE ANOMALY

2005 ◽  
Vol 14 (07) ◽  
pp. 1233-1250 ◽  
Author(s):  
M. FARHOUDI
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Second Order ◽  
Alternative Form ◽  
Mathematical Form ◽  
Einstein’S Field Equations ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy–momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.

scholarly journals A quantum field-theoretical perspective on scale anomalies in 1D systems with three-body interactions

2019 ◽  
Vol 34 (35) ◽  
pp. 1950291 ◽  
Author(s):  
W. S. Daza ◽  
J. E. Drut ◽  
C. L. Lin ◽  
C. R. Ordóñez
Keyword(s):  
Energy Momentum Tensor ◽  
Scattering Amplitude ◽  
Theoretical Perspective ◽  
Dimensional Regularization ◽  
Momentum Tensor ◽  
Quantum Field ◽  
One Dimensional ◽  
Scattering States ◽  
Three Body ◽  
Canonical Quantum

We analyze, from a canonical quantum field theory (QFT) perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional (2D) systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the nonvanishing non-relativistic trace of the energy–momentum tensor.

Renormalization of the energy-momentum tensor and the trace anomaly in lattice QED

1989 ◽  
Vol 228 (3) ◽  
pp. 375-378 ◽  
Author(s):  
Sergio Caracciolo ◽  
Giuseppe Curci ◽  
Pietro Menotti ◽  
Andrea Pelissetto
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Trace Anomaly

Energy-momentum tensor of a massless scalar quantum field in a Robertson-Walker universe

1977 ◽  
Vol 109 (1) ◽  
pp. 108-142 ◽  
Author(s):  
P.C.W. Davies ◽  
S.A. Fulling ◽  
S.M. Christensen ◽  
T.S. Bunch
Keyword(s):  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Quantum Field ◽  
Scalar Quantum

scholarly journals Examining a covariant and renormalizable quantum field theory in de Sitter space by studying “black hole radiation”

2016 ◽  
Vol 31 (11) ◽  
pp. 1650052 ◽  
Author(s):  
Hamed Pejhan ◽  
Surena Rahbardehghan
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
De Sitter ◽  
Black Hole Radiation

Respecting that any consistent quantum field theory in curved space–time must include black hole radiation, in this paper, we examine the Krein–Gupta–Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman–Gärding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy–momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field to vanish. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy–momentum tensor. On this basis, by evaluating the Casimir energy–momentum tensor for a conformally coupled massless scalar field in the vicinity of a nonrotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.

scholarly journals Mass sum rules of the electron in quantum electrodynamics

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
S. Rodini ◽  
A. Metz ◽  
B. Pasquini
Keyword(s):  
Quantum Electrodynamics ◽  
Rest Frame ◽  
Energy Momentum Tensor ◽  
Sum Rules ◽  
Form Factors ◽  
Momentum Tensor ◽  
Moving Frame ◽  
Nucleon Mass ◽  
Loop Order ◽  
The Masses

Abstract Different decompositions of the nucleon mass, in terms of the masses and energies of the underlying constituents, have been proposed in the literature. We explore the corresponding sum rules in quantum electrodynamics for an electron at one-loop order in perturbation theory. To this aim we compute the form factors of the energy-momentum tensor, by paying particular attention to the renormalization of ultraviolet divergences, operator mixing and scheme dependence. We clarify the expressions of all the proposed sum rules in the electron rest frame in terms of renormalized operators. Furthermore, we consider the same sum rules in a moving frame, where they become energy decompositions. Finally, we discuss some implications of our study on the mass sum rules for the nucleon.

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