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.

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.

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 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

scholarly journals Non-trivial effects of sourceless forces for spinors: toward an Aharonov–Bohm gravitational effect?

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Luca Fabbri ◽  
Flora Moulin ◽  
Aurélien Barrau
Keyword(s):  
Hydrogen Atom ◽  
Relativistic Effects ◽  
Gravitational Effect ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Polar Form ◽  
Quantum Field ◽  
Riemann Curvature ◽  
Spinor Fields ◽  
Aharonov Bohm

Abstract Spinor fields are written in polar form so as to compute their tensorial connection, an object that contains the same information of the connection but which is also proven to be a real tensor. From this, one can still compute the Riemann curvature, encoding the information about gravity. But even in absence of gravity, when the Riemann curvature vanishes, it may still be possible that the tensorial connection remains different from zero, and thih can have effects on matter. This is shown with examples in the two known integrable cases: the hydrogen atom and the harmonic oscillator. The fact that a spinor can feel effects due to sourceless actions is already known in electrodynamics as the Aharonov–Bohm phenomenon. A parallel between the electrodynamics case and the situation encountered here will be drawn. Some ideas about relativistic effects and their role for general treatments of quantum field theories are also underlined.

scholarly journals Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

1985 ◽  
Vol 40 (7) ◽  
pp. 752-773
Author(s):  
H. Stumpf
Keyword(s):  
Composite Particle ◽  
Particle Interaction ◽  
High Energy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Statistical Interpretation ◽  
Quantum Field ◽  
Mapping Procedure ◽  
Effective Dynamics ◽  
Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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