Difficulties with the definition of charge in axiomatic quantum field theory

1967 ◽  
Vol 51 (1) ◽  
pp. 128-146 ◽  
Author(s):  
P. de Mottoni
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Definition Of ◽  
Axiomatic Quantum Field Theory

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.

On the "Edge of the Wedge" Theorem

1963 ◽  
Vol 15 ◽  
pp. 125-131 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Complex Variables ◽  
Point Of View ◽  
Several Complex Variables ◽  
Quantum Field ◽  
Complete Proof ◽  
Strategic Role ◽  
Mathematical Justification ◽  
Axiomatic Quantum Field Theory

In the mathematical justification of the formal calculations of axiomatic quantum field theory and the theory of dispersion relations, a strategic role is played by a theorem on analytic functions of several complex variables which has been given the euphonious name of the edge of the wedge theorem. The statement of the theorem seems to be due originally to N. Bogoliubov (cf. 3, Mathematical Appendix, pp. 654-673) but no complete proof which is fully satisfactory from the mathematical point of view has yet appeared in the literature.

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