scholarly journals Towards the Construction of Quantum Field Theories from a Factorizing S-Matrix

2007 ◽  
pp. 175-197 ◽  
Author(s):  
Gandalf Lechner
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
S Matrix

scholarly journals Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Dongmin Gang ◽  
Sungjoon Kim ◽  
Kimyeong Lee ◽  
Myungbo Shim ◽  
Masahito Yamazaki
Keyword(s):  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Superconformal Field Theory ◽  
Three Sphere ◽  
Topological Quantum ◽  
S Matrix ◽  
Modular Data ◽  
Topological Theories

Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

scholarly journals THERMOFIELD DYNAMICS FOR TWISTED POINCARÉ-INVARIANT FIELD THEORIES: WICK THEOREM AND S-MATRIX

2011 ◽  
Vol 26 (15) ◽  
pp. 2569-2589 ◽  
Author(s):  
MARCELO LEINEKER ◽  
AMILCAR R. QUEIROZ ◽  
ADEMIR E. SANTANA ◽  
CHRYSTIAN DE ASSIS SIQUEIRA
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
S Matrix ◽  
Scalar Quantum ◽  
Wick Theorem ◽  
Wick’S Theorem ◽  
Invariant Quantum

Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.

MODULAR CONSTRUCTIONS OF QUANTUM FIELD THEORIES WITH INTERACTIONS

2000 ◽  
Vol 12 (02) ◽  
pp. 301-326 ◽  
Author(s):  
B. SCHROER AKEROYD ◽  
H.-W. WIESBROCK
Keyword(s):  
Fourier Transforms ◽  
Double Cone ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Cone Algebra ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Modular Method ◽  
Quantum Localization

We extend the previously introduced constructive modular method to nonperturbative QFT. In particular the relevance of the concept of "quantum localization" (via intersection of algebras) versus classical locality (via support properties of test functions) is explained in detail, the wedge algebras are constructed rigorously and the formal aspects of double cone algebras for d=1+1 factorizing theories are determined. The well-known on-shell crossing symmetry of the S-Matrix and of formfactors (cyclicity relation) in such theories is intimately related to the KMS properties of new quantum-local PFG (one-particle polarization-free) generators of these wedge algebras. These generators are "on-shell" and their Fourier transforms turn out to fulfill the Zamolodchikov–Faddeev algebra. As the wedge algebras contain the crossing symmetry information, the double cone algebras reveal the particle content of fields. Modular theory associates with this double cone algebra two very useful chiral conformal quantum field theories which are the algebraic versions of the light ray algebras.

scholarly journals FERMION–BOSON DUALITY IN INTEGRABLE QUANTUM FIELD THEORY

1998 ◽  
Vol 13 (35) ◽  
pp. 2807-2818 ◽  
Author(s):  
P. BASEILHAC ◽  
V. A. FATEEV
Keyword(s):  
Scattering Theory ◽  
Field Theories ◽  
Lagrangian Description ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Duality Transformation ◽  
Neutral Particles ◽  
Integrable Quantum ◽  
S Matrix ◽  
Integrable Quantum Field Theory

We introduce and study one-parameter family of integrable quantum field theories. This family has a Lagrangian description in terms of massive Thirring fermions ψ, ψ† and charged bosons χ, [Formula: see text] of complex sinh–Gordon model coupled with BCn affine Toda theory. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are applied to show that under duality transformation, which relates weak and strong coupling regimes of the theory, the fermions ψ, ψ† transform to bosons and χ, [Formula: see text] and vice versa. The scattering amplitudes of neutral particles in this theory coincide exactly with S-matrix of particles in pure BCn Toda theory, i.e. the contribution of charged bosons and fermions to these amplitudes exactly cancel each other. We describe and discuss the symmetry responsible for this compensation property.

scholarly journals Spinning S-matrix bootstrap in 4d

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Aditya Hebbar ◽  
Denis Karateev ◽  
João Penedones
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Bootstrap Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yukawa Couplings ◽  
S Matrix ◽  
Mandelstam Analyticity

Abstract We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

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.

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