scholarly journals CLIFFORD ALGEBRAS IN FINITE QUANTUM FIELD THEORIES I.

1998 ◽  
Vol 13 (13) ◽  
pp. 2047-2073
Author(s):  
WOLFGANG LUCHA ◽  
MICHAEL MOSER
Keyword(s):  
Gauge Coupling ◽  
Field Theories ◽  
Physical Parameters ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Gauge Groups ◽  
Yukawa Couplings ◽  
Simplifying Assumptions ◽  
Gauge Anomalies ◽  
Promising Type

Finite quantum field theories may be constructed from the most general renormalizable quantum field theory by forbidding, order by order in the perturbative loop expansion, all ultraviolet-divergent renormalizations of the physical parameters of the theory. The relevant finiteness conditions resulting from this requirement relate all dimensionless couplings in the theory. At first sight, Yukawa couplings which are equivalent to the generators of some Clifford algebra with identity element represent a very promising type of solutions of the condition for one-loop finiteness of the Yukawa couplings. However, under a few reasonable and simplifying assumptions about their particular structure, these Clifford-like Yukawa couplings prove to be in conflict with the requirements of one- and two-loop finiteness of the gauge coupling and of the absence of gauge anomalies, at least for all simple gauge groups up to and including rank 8.

scholarly journals TOWARDS FINITENESS WITHOUT SUPERSYMMETRY

1994 ◽  
Vol 09 (05) ◽  
pp. 711-726 ◽  
Author(s):  
HARALD SKARKE
Keyword(s):  
Gauge Coupling ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Yukawa Couplings

Some aspects of finite quantum field theories in 3+1 dimensions are discussed. A model with nonsupersymmetric particle content and vanishing one- and two-loop beta functions for the gauge coupling and one-loop beta functions for Yukawa couplings is presented.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

scholarly journals ON NON-SUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES

1995 ◽  
Vol 10 (10) ◽  
pp. 1507-1528
Author(s):  
PETER GRANDITS
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Gauge Coupling ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Scalar Couplings ◽  
Finiteness Conditions ◽  
Yukawa Couplings ◽  
Loop Approximation ◽  
Supersymmetric Gauge

In a previous paper, requiring finiteness of Yukawa couplings in one-loop approximation, a no-go theorem for the finiteness of non-supersymmetric gauge theories with gauge group SU (n) was proven. Interestingly enough the gauge group SU(5), prominent in GUT models, was not covered by this proof. However, with somewhat more effort the no-go theorem can be extended to this case. Considering an even larger class of particle contents, we show that the number of possibly finite theories is greatly reduced. It should be stressed that our results are based upon two-loop finiteness of the gauge coupling, although in order to find really finite theories the finiteness conditions on the quartic scalar couplings have to be considered too.

NO-GO THEOREMS FOR NONSUPERSYMMETRIC FINITE QUANTUM FIELD THEORIES

1994 ◽  
Vol 09 (12) ◽  
pp. 1093-1103 ◽  
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Invariance ◽  
Field Theories ◽  
Special Role ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Finiteness Conditions ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for groups SU (N). Their gauge invariance leads us to the necessary structure of the couplings, and for some cases the nonexistence of non-trivial solutions is proved. Somewhat miraculously a special role of SU(5) emerges as a possible case of evading these no-go theorems.

scholarly journals a×b=c in 2+1D TQFT

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 468
Author(s):  
Matthew Buican ◽  
Linfeng Li ◽  
Rajath Radhakrishnan
Keyword(s):  
Gauge Theories ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Mathieu Group ◽  
Gauge Groups ◽  
Global Properties ◽  
Topological Quantum ◽  
The One ◽  
Chern Simons

We study the implications of the anyon fusion equation a×b=c on global properties of 2+1D topological quantum field theories (TQFTs). Here a and b are anyons that fuse together to give a unique anyon, c. As is well known, when at least one of a and b is abelian, such equations describe aspects of the one-form symmetry of the theory. When a and b are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and a and b lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian a and b can also be an indication of zero-form symmetries in a TQFT, of what we term "quasi-zero-form symmetries" (as in the case of discrete gauge theories based on the largest Mathieu group, M24), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.

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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