ORTHOPOSITRONIUM LIFETIME PROBLEM

1993 ◽  
Vol 08 (17) ◽  
pp. 2859-2874 ◽  
Author(s):  
M. I. DOBROLIUBOV ◽  
S. N. GNINENKO ◽  
A. YU. IGNATIEV ◽  
V. A. MATVEEV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Standard Treatment ◽  
Bound State ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
State Problem ◽  
Decay Modes ◽  
Experimental Values ◽  
Bound State Problem

We review the present status of the problem of the six standard deviation discrepancy between the theoretical and experimental values of the orthopositronium lifetime. We discuss possible ways of its explanation and show that those invoking new decay modes are apparently closed. So the solution of this problem most probably lies either in large numerical value of the next, yet uncalculated, coefficient in the perturbative expansion of the orthopositronium decay width or in shortcomings of the standard treatment of the bound state problem in quantum field theory.

scholarly journals Resonance Electroproduction and the Origin of Mass

2020 ◽  
Vol 241 ◽  
pp. 02008
Author(s):  
Craig D. Roberts
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Bound State ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
State Problem ◽  
The Standard Model ◽  
Bound State Problem ◽  
The Continuum

One of the greatest challenges within the Standard Model is to discover the source of visible mass. Indeed, this is the focus of a “Millennium Problem”, posed by the Clay Mathematics Institute. The answer is hidden within quantum chromodynamics (QCD); and it is probable that revealing the origin of mass will also explain the nature of confinement. In connection with these issues, this perspective will describe insights that have recently been drawn using contemporary methods for solving the continuum bound-state problem in relativistic quantum field theory and how they have been informed and enabled by modern experiments on nucleon-resonance electroproduction.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

Field theory: Perturbative expansion and summation methods

2019 ◽  
pp. 451-470
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Conformal Mapping ◽  
Critical Exponents ◽  
Perturbative Expansion ◽  
Divergent Series ◽  
Quantum Field ◽  
Summation Methods ◽  
Borel Transformation

Chapter 23 examines perturbative expansion and summation methods in field theory. In quantum field theory, all perturbative expansions are divergent series in the mathematical sense. This leads to a difficulty when the expansion parameter is not small. In the case of Borel summable series, using the knowledge of the large order behaviour, a number of summation techniques have been developed to derive convergent sequences from divergent series. Some methods apply directly on the series like Padé approximants or order–dependent mapping (the ODM method). Others involve first a Borel transformation, like the Padé–Borel method. The method of Borel transformation, suitably modified, followed by a conformal mapping, has been applied to renormalization group (RG) functions of the phi4 3 field theory and has led to precise values of critical exponents.

The Norms of Multimass States in Relativistic Quantum Field Theory

1974 ◽  
Vol 52 (20) ◽  
pp. 1988-1994 ◽  
Author(s):  
Roger Palmer ◽  
Yasushi Takahashi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Bound State ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Negative Norm ◽  
Quantum Numbers ◽  
Multimass System ◽  
Dynamical Origin

We examined the problem of the appearance of negative norm states in multimass models. It is shown explicitly how the bound state with the same quantum numbers as the elementary meson, can acquire the positive norm. It is inferred from our argument that the multimass system of dynamical origin can be quantized without the negative norm, contrary to the multimass system of kinematical origin.

scholarly journals EXACT-PROPAGATOR INSTANTANEOUS BETHE–SALPETER EQUATION FOR QUARK–ANTIQUARK BOUND STATES

2006 ◽  
Vol 21 (21) ◽  
pp. 1657-1673 ◽  
Author(s):  
ZHI-FENG LI ◽  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Bound State ◽  
State Equation ◽  
Wave Functions ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Instantaneous Approximation

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement for the solutions of this bound-state equation, i.e. the spectrum of the mass eigenvalues of its bound states and the corresponding wave functions, when considering the quark propagators arising in quantum chromodynamics are explored.

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