scholarly journals Towards general scalar-Yukawa renormalisation group equations at three-loop order

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Tom Steudtner
Keyword(s):  
Renormalisation Group ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Loop Order ◽  
Anomalous Dimensions ◽  
Fermion Masses ◽  
Group Evolution ◽  
General Scalar ◽  
Mass Terms

Abstract For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme are investigated at three-loop order in perturbation theory. Collecting literature results, general expressions are obtained for field anomalous dimensions, Yukawa interactions, as well as fermion masses. The renormalisation group evolution of scalar quartic, cubic and mass terms is determined up to a few unknown coefficients. The combined results are applied to compute the renormalisation group evolution of the gaugeless Litim-Sannino model.

scholarly journals General scalar renormalisation group equations at three-loop order

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Tom Steudtner
Keyword(s):  
Specific Model ◽  
Renormalisation Group ◽  
Loop Order ◽  
Four Dimensions ◽  
Anomalous Dimensions ◽  
General Scalar ◽  
Mass Terms ◽  
Scalar Theories

Abstract For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

scholarly journals Perturbative Peculiarities of Quantum Field Theories at High Temperatures

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 81
Author(s):  
Ingolf Bischer ◽  
Thierry Grandou ◽  
Ralf Hofmann
Keyword(s):  
Perturbation Theory ◽  
Thermal Equilibrium ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Zero Temperature ◽  
Thermal Perturbation ◽  
Loop Order ◽  
Damping Rate ◽  
Rate Calculation

Revisiting the fast fermion damping rate calculation in a thermalized QED and/or QCD plasma in thermal equilibrium at four-loop order, focus is put on a peculiar perturbative structure which has no equivalent at zero-temperature. Not surprisingly, and in agreement with previous C ☆ -algebraic analyses, this structure renders the use of thermal perturbation theory more than questionable.

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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