NEW PERTURBATIVE APPROACH TO GENERAL RENORMALIZABLE QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (19) ◽  
pp. 3381-3397 ◽  
Author(s):  
V. GUPTA ◽  
D.V. SHIRKOV ◽  
O.V. TARASOV
Keyword(s):  
Renormalization Group ◽  
Perturbation Expansion ◽  
Renormalization Scheme ◽  
Coupling Constants ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Perturbative Approach ◽  
Coupling Case

We develop further the new approach to perturbation theory for renormalizable quantum field theories (proposed some years ago) which gives renormalization-scheme-independent predictions for observable quantities. We call the resulting REnormalization-Scheme-Independent PErturba-tion theory RESIPE, for short. First, we formulate explicitly the relation of RESIPE to the renormalization group formalism for the massless one-coupling case. Then we extend this to the case where particle masses cannot be neglected. Further, we generalize the RESIPE formalism for the theory with two coupling constants. A new scheme-invariant perturbation expansion, without reference to renormalization group techniques, is given which is valid for the general case with masses, several kinematic variables and more than one coupling constant. In conclusion, we argue that the appropriately generalized RESIPE provides us with a picture of perturbative predictions, for renormalizable quantum field theories, that is free from regularization and renormalization scheme ambiguities.

scholarly journals Beta functions in the quantum field theory

2022 ◽  
Vol 70 (1) ◽  
pp. 157-168
Author(s):  
Nikola Fabiano
Keyword(s):  
Field Theory ◽  
Quantum Electrodynamics ◽  
Beta Function ◽  
Coupling Constants ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
High Energies

Introduction/purpose: The running of the coupling constant in various Quantum Field Theories and a possible behaviour of the beta function are illustrated. Methods: The Callan-Symanzik equation is used for the study of the beta function evolution. Results: Different behaviours of the coupling constant for high energies are observed for different theories. The phenomenon of asymptotic freedom is of particular interest. Conclusions: Quantum Electrodynamics (QED) and Quantum Chromodinamics (QCD) coupling constants have completely different behaviours in the regime of high energies. While the first one diverges for finite energies, the latter one tends to zero as energy increases. This QCD phenomenon is called asymptotic freedom.

The Principles of Renormalisation

2021 ◽  
pp. 304-328
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Power Counting ◽  
Field Theories ◽  
Asymptotic Freedom ◽  
Green Functions ◽  
Quantum Field Theories ◽  
Quantum Field

Loop diagrams often yield ultraviolet divergent integrals. We introduce the concept of one-particle irreducible diagrams and develop the power counting argument which makes possible the classification of quantum field theories into non-renormalisable, renormalisable and super-renormalisable. We describe some regularisation schemes with particular emphasis on dimensional regularisation. The renormalisation programme is described at one loop order for φ‎4 and QED. We argue, without presenting the detailed proof, that the programme can be extended to any finite order in the perturbation expansion for every renormalisable (or super-renormalisable) quantum field theory. We derive the equation of the renormalisation group and explain how it can be used in order to study the asymptotic behaviour of Green functions. This makes it possible to introduce the concept of asymptotic freedom.

Estimates on Renormalization Group Transformations

1998 ◽  
Vol 50 (4) ◽  
pp. 756-793 ◽  
Author(s):  
D. Brydges ◽  
J. Dimock ◽  
T. R. Hurd
Keyword(s):  
Renormalization Group ◽  
Gaussian Measure ◽  
Ultra Violet ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
Scalar Quantum ◽  
Polymer Expansion ◽  
Renormalization Group Flows

AbstractWe consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.

scholarly journals RENORMALIZATION WITHOUT INFINITIES

2005 ◽  
Vol 20 (06) ◽  
pp. 1336-1345 ◽  
Author(s):  
GERARD 'T HOOFT
Keyword(s):  
Renormalization Group ◽  
Conceptual Understanding ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Renormalization Group Equations

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous "paths" in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities.

scholarly journals Complementary projection defects and decomposition

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Correlation Functions ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Renormalization Group Flows ◽  
Topological Quantum Field Theories

Abstract As put forward in [1] topological quantum field theories can be projected using so-called projection defects. The projected theory and its correlation functions can be completely realized within the unprojected one. An interesting example is the case of topological quantum field theories associated to IR fixed points of renormalization group flows, which by this method can be realized inside the theories associated to the UV. In this note we show that projection defects in triangulated defect categories (such as defects in 2d topologically twisted $$ \mathcal{N} $$ N = (2, 2) theories) always come with complementary projection defects, and that the unprojected theory decomposes into the theories associated to the two projection defects. We demonstrate this in the context of Landau-Ginzburg orbifold theories.

scholarly journals Tensor Renormalization Group for interacting quantum fields

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 586
Author(s):  
Manuel Campos ◽  
German Sierra ◽  
Esperanza Lopez
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Real Space ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Excellent Performance ◽  
Tensor Network ◽  
Feynman Graphs

We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a λϕ4 theory for benchmark, we evaluate the order λ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.

DYSON-SCHWINGER EQUATIONS IN TERMS OF RANDOM WALKS: FOUR-FERMION INTERACTIONS

1993 ◽  
Vol 08 (27) ◽  
pp. 4915-4935
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Random Walks ◽  
Physical Interpretation ◽  
Equations Of Motion ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Coupling Constant ◽  
Gap Equation ◽  
Starting Point ◽  
Bare Coupling Constant

Quantum field theories of interacting fermions have been recently formulated in terms of directed random walks. Using this formulation, we derive a hierarchy of equations for the correlation functions of scalar N-component four-fermion theories. These follow from an analysis of the underlying random process, and from geometric considerations. Our equations are, as we show, equivalent to the standard Dyson-Schwinger equations of motion, and are a convenient starting point for nonperturbative investigations of four-fermion theories. In particular, we discuss the physical interpretation of the gap equation in the language of random walks, and show that, in both the N→0 and N→∞ limits, an interacting theory can be obtained only for a finely tuned negative bare coupling constant.

scholarly journals DISCRETE QUANTUM FIELD THEORIES AND THE INTERSECTION FORM

1994 ◽  
Vol 09 (24) ◽  
pp. 2265-2271 ◽  
Author(s):  
DANNY BIRMINGHAM ◽  
MARK RAKOWSKI
Keyword(s):  
Cohomology Group ◽  
Lattice Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Explicit Computation ◽  
Coupling Constant ◽  
Intersection Form ◽  
Dimensional Model ◽  
Mod P

It is shown that the standard mod-p valued intersection form can be used to define Boltzmann weights of subdivision invariant lattice models with gauge group Zp. In particular, we discuss a four-dimensional model which is based on the assignment of field variables to the two-simplices of the simplicial complex. The action is taken to be the intersection form defined on the second cohomology group of the complex, with coefficients in Zp. Subdivision invariance of the theory follows when the coupling constant is quantized and the field configurations are restricted to those satisfying a mod-p flatness condition. We present an explicit computation of the partition function for the manifold ± CP 2, demonstrating non-triviality.

scholarly journals Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1221
Author(s):  
Satoshi Iso ◽  
Takato Mori ◽  
Katsuta Sakai
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Effective Action ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

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