The definition of local observables in quantum field theory

1969 ◽  
Vol 63 (1) ◽  
pp. 236-240 ◽  
Author(s):  
A. Z. Capri
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Local Observables ◽  
Definition Of

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.

STABLE QUASIPARTICLE PICTURE IN THERMAL QUANTUM FIELD PHYSICS

1994 ◽  
Vol 09 (10) ◽  
pp. 1703-1729 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Quantum Field ◽  
Self Energy ◽  
Vector Algebra ◽  
Physical Particle ◽  
Usual Quantum ◽  
Definition Of

It is well known that physical particles are thermally dissipative at finite temperature. In this paper we reformulate both the equilibrium and nonequilibrium thermal field theories in terms of stable quasiparticles. We will redefine the thermal doublets, the double tilde conjugation rules and the thermal Bogoliubov transformations so that our theory can be consistent for most general situations. All operators, including the dissipative physical particle operators, are realized in a Fock space defined by the stable quasiparticles. The propagators of the physical particles are expressed in terms of the operators of such stable quasiparticles, which is a simple diagonal matrix with the diagonal elements being the temporal step functions, same as the propagators in the usual quantum field theory without thermal degrees of freedom. The proper self-energies are also expressed in terms of these stable quasiparticle propagators. This formalism inherits the definition of on-shell self-energy in the usual quantum field theory. With this definition, a self-consistent renormalization is formulated which leads to quantum Boltzmann equation and the entropy law. With the aid of a doublet vector algebra we have an extremely simple recipe for computing Feynman diagrams. We apply this recipe to several examples of equilibrium and nonequilibrium two-point functions, and to the kinetic equation for the particle numbers.

scholarly journals A note on oscillating neutrino states in quantum field theory

2020 ◽  
Vol 35 (38) ◽  
pp. 2050313
Author(s):  
Massimo Blasone ◽  
Luca Smaldone
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Physical Vacuum ◽  
Quantum Field ◽  
Definition Of

In a recent paper [Eur. Phys. J. C 80, 68 (2020)], a definition of oscillating neutrino states in quantum field theory was proposed. We show that such definition can be derived as a particular case of the Blasone–Vitiello approach, when mass vacuum is chosen as the physical vacuum. We discuss some problems of such an approach, which appears to be mathematically inconsistent and physically not acceptable.

scholarly journals Functorial Evolution of Quantum Fields

2021 ◽  
Vol 9 ◽  
Author(s):  
Stefano Gogioso ◽  
Maria E. Stasinou ◽  
Bob Coecke
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cellular Automata ◽  
Quantum Field ◽  
Quantum Fields ◽  
Causal Order ◽  
Algebraic Quantum ◽  
Starting Point ◽  
Algebraic Framework ◽  
Definition Of

We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory.

scholarly journals Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 504
Author(s):  
Luca Smaldone ◽  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Dynamical Symmetry ◽  
Neutrino Energy ◽  
Uncertainty Relations ◽  
Quantum Field ◽  
Neutrino Mixing ◽  
Relativistic Limit ◽  
Definition Of

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.

scholarly journals PHASE SPACE PROPERTIES OF CHARGED FIELDS IN THEORIES OF LOCAL OBSERVABLES

1995 ◽  
Vol 07 (04) ◽  
pp. 527-557 ◽  
Author(s):  
D. BUCHHOLZ ◽  
C. D’ANTONI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Space ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Space Analysis ◽  
Algebraic Quantum ◽  
Thermal Features ◽  
Local Observables

Within the setting of algebraic quantum field theory a relation between phase-space properties of observables and charged fields is established. These properties are expressed in terms of compactness and nuclearity conditions which are the basis for the characterization of theories with physically reasonable causal and thermal features. Relevant concepts and results of phase space analysis in algebraic quantum field theory are reviewed and the underlying ideas are outlined.

scholarly journals On the Foundations of Statistical Nuclear Physics

2020 ◽  
Vol 1 ◽  
pp. 179
Author(s):  
C. Syros
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Nuclear Physics ◽  
Canonical Ensemble ◽  
Quantum Field ◽  
Definition Of

The density matric for the nucleus, the canonical ensemble in second quantized mechanical definition of the temperature have from Quantum Field Theory. The evolution conservative or dissipalive form and is ergodic.

scholarly journals Toward a Definition of Complexity for Quantum Field Theory States

2018 ◽  
Vol 120 (12) ◽  
Author(s):  
Shira Chapman ◽  
Michal P. Heller ◽  
Hugo Marrochio ◽  
Fernando Pastawski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Definition Of
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