scholarly journals New regulators for quantum field theories with compactified extra dimensions. II. Ultraviolet finiteness and effective field theory implementation

2008 ◽  
Vol 77 (12) ◽  
Author(s):  
Sky Bauman ◽  
Keith R. Dienes
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Extra Dimensions ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field

Quantum field theory: An effective theory

2019 ◽  
pp. 111-136
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Statistical Physics ◽  
Mass Scale ◽  
Effective Field ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Microscopic Scale ◽  
Linear Sigma Models

Chapter 8 discusses effective field theory. This concept is inspired by the theory of critical phenomena in statistical physics and based on renormalization group ideas. The basic idea behind effective field theory is that one starts from a microscopic model involving an infinite number of fluctuating degrees of freedom whose interactions are characterized by a microscopic scale and in which, as a result of interactions, a length that is much larger than the microscopic scale, or, equivalently, a mass much smaller than the characteristic mass scale of the initial model, is generated. The chapter illustrates this topic with examples. It also stresses that all quantum field theories as applied to particle physics or statistical physics are only effective (i.e. not fundamental) theories. Besides the problem of a phi4 type field theory with a large mass field, two more complicated examples are discussed: the Gross–Neveu and the non–linear sigma models.

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

Renormalization Theory and Effective Field Theories

2020 ◽  
pp. 1-46
Author(s):  
Matthias Neubert
Keyword(s):  
Field Theory ◽  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Effective Theories ◽  
Renormalization Theory ◽  
Scale Evolution

Chapter 1 features lectures that review the formalism of renormalization in quantum field theories with special regard to effective quantum field theories. While renormalization theory is part of every advanced course on quantum field theory, for effective theories some more advanced topics become particularly important. These topics include the renormalization of composite operators, operator mixing under scale evolution, and the resummation of large logarithms of scale ratios. The lectures from this course thus set the basis for any systematic study of the techniques and applications of effective field theories and offer an introduction for the reader to the content within this book.

scholarly journals THE CONDITION 0 < Z < 1 AND AN INTRINSIC MASS SCALE IN QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (27) ◽  
pp. 4489-4497 ◽  
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Field Theory ◽  
Mass Scale ◽  
Effective Field ◽  
Energy Scale ◽  
Field Theories ◽  
Beyond The Standard Model ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Nonlocal Formulation ◽  
Intrinsic Scale

In this work, we suggest a viewpoint that leads to an intrinsic mass scale in quantum field theories. This viewpoint is fairly independent of dynamical details of a QFT and does not rely on any particular framework to go beyond the Standard Model. We use the setting of the nonlocal quantum field theories (NLQFT) with a finite scale parameter Λ, which are unitary for finite Λ. We propose that the condition 0 < Z < 1 (wherever proven) can be rigorously implemented/imposed in such theories and that it implies the existence of a mass scale Λ that can be determined from this condition. We derive the nonlocal analog of the above relation (which is a finite relation in NLQFT) and demonstrate that it can be arrived at only from general principles. We further propose that the nonlocal formulation should be looked as an effective field theory that incorporates the effect of dynamics beyond an energy scale and which breaks at the intrinsic scale Λ so obtained. Beyond this scale it should be replaced by another (perhaps, a more fundamental) theory. We provide a heuristic justification for this viewpoint.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

scholarly journals Quantum Field Theory over $\mathbb{F}_q$

10.37236/589 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Oliver Schnetz
Keyword(s):  
Field Theory ◽  
Perturbation Series ◽  
The Other ◽  
Field Theories ◽  
Roots Of Unity ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Graph Hypersurfaces ◽  
Prime 2

We consider the number $\bar N(q)$ of points in the projective complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give six examples which fall into two classes. One class has an exceptional prime 2 whereas in the other class $\bar N(q)$ depends on the number of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$ times the number of points in the projective complement of a singular K3 in $\mathbb{P}^3$. In the second part of the paper we show that applying momentum space Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate for renormalizable and non-renormalizable bosonic quantum field theories.

scholarly journals ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES

1999 ◽  
Vol 08 (02) ◽  
pp. 125-163 ◽  
Author(s):  
Louis Crane ◽  
David Yetter
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hopf Algebra ◽  
Tensor Category ◽  
Topological Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Topological Quantum ◽  
Natural Way

We show that any 3D topological quantum field theory satisfying physically reasonable factorizability conditions has associated to it in a natural way a Hopf algebra object in a suitable tensor category. We also show that all objects in the tensor category have the structure of left-left crossed bimodules over the Hopf algebra object. For 4D factorizable topological quantum filed theories, we provide by analogous methods a construction of a Hopf algebra category.

Integrable Quantum Field Theories

2020 ◽  
pp. 575-621
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Two Dimensional ◽  
Conformal Theory ◽  
Integrable Quantum ◽  
Set Up ◽  
Integrable Quantum Field Theory

Chapter 16 covers the general properties of the integrable quantum field theories, including how an integrable quantum field theory is characterized by an infinite number of conserved charges. These theories are illustrated by means of significant examples, such as the Sine–Gordon model or the Toda field theories based on the simple roots of a Lie algebra. For the deformations of a conformal theory, it shown how to set up an efficient counting algorithm to prove the integrability of the corresponding model. The chapter focuses on two-dimensional models, and uses the term ‘two-dimensional’ to denote both a generic two-dimensional quantum field theory as well as its Euclidean version.

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.

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