Calculation of critical exponents in two dimensions from quantum field theory in one dimension

1975 ◽  
Vol 12 (9) ◽  
pp. 3908-3917 ◽  
Author(s):  
A. Luther ◽  
I. Peschel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Critical Exponents ◽  
Two Dimensions ◽  
One Dimension ◽  
Quantum Field

Quantization and topology: SL(2,R)-de Sitter invariant fields in two dimensions

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040018
Author(s):  
Henri Epstein ◽  
Ugo Moschella
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
De Sitter ◽  
Cosmological Background ◽  
Local Commutativity ◽  
And Topology ◽  
The Many

We explore the interplay between quantization, local commutativity and the analyticity properties of the two-point functions of a quantum field in a non trivial topological cosmological background in the example of the two-dimensional de Sitter manifold and its double covering. The global topological differences make the many of the well-known features of de Sitter quantum field theory disappear. In particular there is nothing like a Bunch-Davies vacuum and there are no [Formula: see text]-invariant fields whose mass is less than 1/2.

Field theory: Perturbative expansion and summation methods

2019 ◽  
pp. 451-470
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Conformal Mapping ◽  
Critical Exponents ◽  
Perturbative Expansion ◽  
Divergent Series ◽  
Quantum Field ◽  
Summation Methods ◽  
Borel Transformation

Chapter 23 examines perturbative expansion and summation methods in field theory. In quantum field theory, all perturbative expansions are divergent series in the mathematical sense. This leads to a difficulty when the expansion parameter is not small. In the case of Borel summable series, using the knowledge of the large order behaviour, a number of summation techniques have been developed to derive convergent sequences from divergent series. Some methods apply directly on the series like Padé approximants or order–dependent mapping (the ODM method). Others involve first a Borel transformation, like the Padé–Borel method. The method of Borel transformation, suitably modified, followed by a conformal mapping, has been applied to renormalization group (RG) functions of the phi4 3 field theory and has led to precise values of critical exponents.

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

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