scholarly journals THERMODYNAMIC BETHE ANSATZ AND THREE-FOLD TRIANGULATIONS

1996 ◽  
Vol 11 (22) ◽  
pp. 4051-4064 ◽  
Author(s):  
F. GLIOZZI ◽  
R. TATEO
Keyword(s):  
Bethe Ansatz ◽  
Unknown Function ◽  
Functional Equations ◽  
Simple Solution ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Thermodynamic Bethe Ansatz ◽  
Ansatz Approach ◽  
General Explanation

In the thermodynamic Bethe ansatz approach to 2D integrable, ADE-related quantum field theories, one derives a set of algebraic functional equations (a Y system) which play a prominent role. This set of equations is mapped onto the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y system. For the AN related theories, and more generally for the various restrictions of the fractionally supersymmetric sine—Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently found dilogarithm functional equations associated to the Y system simply express the invariance of the volume of a manifold for deformations of its triangulations.

scholarly journals The Bethe ansatz and the Tzitzéica–Bullough–Dodd equation

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120052 ◽  
Author(s):  
Patrick Dorey ◽  
Simone Faldella ◽  
Stefano Negro ◽  
Roberto Tateo
Keyword(s):  
Bethe Ansatz ◽  
Nonlinear Wave ◽  
Physical Interpretation ◽  
Wave Equations ◽  
Field Theories ◽  
Nonlinear Wave Equations ◽  
Infinite Cylinder ◽  
Quantum Field Theories ◽  
Quantum Field

The theory of classically integrable nonlinear wave equations and the Bethe ansatz systems describing massive quantum field theories defined on an infinite cylinder are related by an important mathematical correspondence that still lacks a satisfactory physical interpretation. In this paper, we shall extend this link to the case of the classical and quantum versions of the Tzitzéica–Bullough–Dodd model.

scholarly journals A TOPOLOGICAL INVARIANT OF RG FLOWS IN 2D INTEGRABLE QUANTUM FIELD THEORIES

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2927-2932 ◽  
Author(s):  
R. CARACCIOLO ◽  
F. GLIOZZI ◽  
R. TATEO
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Three Dimensional ◽  
Topological Invariant ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Integrable Quantum ◽  
Quantum Integrable Models ◽  
Ansatz Approach

We construct a topological invariant of the renormalization group trajectories of a large class of 2D quantum integrable models, described by the thermodynamic Bethe ansatz approach. A geometrical description of this invariant in terms of triangulations of three-dimensional manifolds is proposed and associated dilogarithm identities are proven.

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.

scholarly journals Categorification of algebraic quantum field theories

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel ◽  
Lukas Woike
Keyword(s):  
Universal Algebra ◽  
Finite Groups ◽  
Physical Interpretation ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Quantum

AbstractThis paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

scholarly journals Applying the Variational Principle to (1+1)-Dimensional Quantum Field Theories

2010 ◽  
Vol 105 (25) ◽  
Author(s):  
Jutho Haegeman ◽  
J. Ignacio Cirac ◽  
Tobias J. Osborne ◽  
Henri Verschelde ◽  
Frank Verstraete
Keyword(s):  
Variational Principle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field
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