Bound states and the effective potential in field theories

1975 ◽  
Vol 12 (4) ◽  
pp. 1178-1191 ◽  
Author(s):  
Richard W. Haymaker
Keyword(s):  
Effective Potential ◽  
Bound States ◽  
Field Theories

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.

scholarly journals BOUNDARY BOUND STATES IN AFFINE TODA FIELD THEORY

1995 ◽  
Vol 10 (05) ◽  
pp. 739-751 ◽  
Author(s):  
ANDREAS FRING ◽  
ROLAND KÖBERLE
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Dynkin Diagram ◽  
Binding Energies ◽  
Field Theories ◽  
Complete Set ◽  
Reflecting Boundaries ◽  
Toda Field Theory

We demonstrate that the generalization of the Coleman–Thun mechanism may be applied to the situation where one considers scattering processes in 1 + 1 dimensions in the presence of reflecting boundaries. For affine Toda field theories we find that the binding energies of the bound states are always half the sum over a set of masses having the same color with respect to the bicoloration of the Dynkin diagram. For the case of E6 affine Toda field theory we compute explicitly the spectrum of all higher boundary bound states. The complete set of states constitutes a closed bootstrap.

scholarly journals Duality and Integrability in Superstring and Gauge Field Theory

2021 ◽  
Author(s):  
◽  
Konstantinos Filippas
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Bound States ◽  
Galois Theory ◽  
Field Theories ◽  
Gauge Field Theory ◽  
Differential Galois Theory ◽  
De Sitter ◽  
Algebraic Form ◽  
Integrable Dynamics

In the present thesis, we explore certain aspects of superstring and supersymmetric gauge field theory, independently as well as in the context of the holographic duality.The first part of the thesis is devoted to classical integrability and, in particular, to certain methods of analytic non-integrability, which are employed on various supergravity vacua. In Chapter 1, we introduce those tools of non-integrability, which consist of choosing an appro-priate string embedding and using differential Galois theory on the associated Hamiltonian system. The arena of all this, for the first chapter, is two classes of vacua in massive Type IIA supergravity, all of which are proven to be non-integrable, up to the trivial cases where the vacuum reduces to the Abelian and non-Abelian T-dual of known integrable backgrounds. Differential Galois theory, in this context, reduces to an algebraic form through Kovacic’s theorem, the proper use of which, on parametrized differential equations, is clarified in this application.In Chapter 2, we study integrability on the supergravity vacuum dual to the field-theoretical Ω-deformation of super Yang-Mills theory. The deformation manifests itself as turning on a Kalb-Ramond field on the dual supergravity vacuum and, by constructing appropriate string embeddings, we show that this space exhibits non-integrable dynamics. This, in turn, suggests that the Ω-deformation does not preserve classical integrability.In Chapter 3, we explore integrability on vacua in massive Type IIA supergravity, dual to six-dimensional superconformal quiver field theories. Analytic non-integrability illustrates that all vacua with a warped geometry, between Anti-de-Sitter space and the internal man-ifold, exhibit complete non-integrability, while in the special case of the unwarped space we prove the opposite to be true. In particular, we show that, besides the integrable dynamics on the symmetric Anti-de-Sitter subspace of the unwarped geometry, the σ-model on the internal manifold is an integrable deformation of the same model on the symmetric three-sphere, ultimately implying classical integrability of bosonic string theory on this special vacuum.The second part of the thesis is devoted to holography and, in particular, the AdS/CFT duality, which we exploit to study features of certain supersymmetric quantum field theories in two spacetime dimensions. More precisely, in Chapter 4, the final chapter, we study the duality between massive Type IIA supergravity vacua and two-dimensional quiver structures. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space which provide the dual quiver theory with exactly the correct amount of matter in order to cancel its gauge anomalies. We also propose that the structure of the field theory should be complemented with additional bifundamental matter and, finally, we construct a BPS string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator.

HALO EFFECTIVE FIELD THEORY

2005 ◽  
Vol 14 (01) ◽  
pp. 11-19
Author(s):  
U. VAN KOLCK
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field Theory ◽  
Bound States ◽  
Effective Field ◽  
Field Theories ◽  
Alpha Scattering

I discuss effective field theories for bound states and narrow resonances near two-body thresholds. I illustrate the method in the case of nucleon-alpha scattering.

scholarly journals Bound states of little strings and symmetric orbifold conformal field theories

2017 ◽  
Vol 96 (8) ◽  
Author(s):  
Ambreen Ahmed ◽  
Stefan Hohenegger ◽  
Amer Iqbal ◽  
Soo-Jong Rey
Keyword(s):  
Bound States ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field
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