scholarly journals 2-Particle asymptotic completeness and bound states in weakly coupled quantum field theories

1988 ◽  
Vol 119 (2) ◽  
pp. 331-351 ◽  
Author(s):  
J. Bros ◽  
D. Iagolnitzer
Keyword(s):  
Bound States ◽  
Asymptotic Completeness ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Weakly Coupled

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals REVIEW OF THE N-QUANTUM APPROACH TO BOUND STATES

2011 ◽  
Vol 26 (06) ◽  
pp. 935-945 ◽  
Author(s):  
O. W. GREENBERG
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
Bound State ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotic Field ◽  
Quantum Approach ◽  
Future Work ◽  
Asymptotic Fields

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.

BINDING ENERGIES IN WEAKLY COUPLED (2+1)-DIMENSIONAL QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (29) ◽  
pp. 2705-2711
Author(s):  
G. GAT ◽  
B. ROSENSTEIN
Keyword(s):  
Perturbation Theory ◽  
Binding Energy ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
General Question ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Weakly Coupled ◽  
Gross Neveu Model

We calculate the binding energy of the two-particle threshold bound state in the (2+1)-dimensional Gross-Neveu model. This model was recently shown to be renormalizable within the 1/N expansion. The binding energy is found to be ΔE=4mc-8Nf where m is the mass of the elementary fermion and Nf is the number of flavors. The general question of consistency of the perturbation theory within the framework of the Bethe-Salpeter equation is discussed.

scholarly journals Global aspects of spaces of vacua

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Adar Sharon
Keyword(s):  
Closed Loop ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Weakly Coupled

Abstract We study “vacuum crossing”, which occurs when the vacua of a theory are exchanged as we vary some periodic parameter θ in a closed loop. We show that vacuum crossing is a useful non-perturbative tool to study strongly-coupled quantum field theories, since finding vacuum crossing in a weakly-coupled regime of the theory can lead to nontrivial consequences in the strongly-coupled regime. We start by discussing a mechanism where vacuum crossing occurs due to an anomaly, and then discuss some applications of vacuum crossing in general. In particular, we argue that vacuum crossing can be used to check IR dualities and to look for emergent IR symmetries.

scholarly journals CASIMIR EFFECTS IN RENORMALIZABLE QUANTUM FIELD THEORIES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 846-869 ◽  
Author(s):  
NOAH GRAHAM ◽  
ROBERT L. JAFFE ◽  
HERBERT WEIGEL
Keyword(s):  
Density Of States ◽  
Bound States ◽  
Phase Shifts ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scattering States ◽  
Extended Field ◽  
The Continuum

We present a framework for the study of one–loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.

scholarly journals Bound states of non-Hermitian quantum field theories

2001 ◽  
Vol 291 (4-5) ◽  
pp. 197-202 ◽  
Author(s):  
Carl M Bender ◽  
Stefan Boettcher ◽  
H.F Jones ◽  
Peter N Meisinger ◽  
Mehmet Şimşek
Keyword(s):  
Bound States ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field
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