On the determination of the field operator representation in canonical model quantum field theory

1973 ◽  
Vol 14 (4) ◽  
pp. 781-811
Author(s):  
T. T. Truong
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Operator ◽  
Canonical Model ◽  
Quantum Field ◽  
Operator Representation

Renormalization Group: From a general concept to numbers

2019 ◽  
pp. 69-80
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
General Concept ◽  
Quantum Field ◽  
Fixed Dimension ◽  
Perturbative Renormalization ◽  
Borel Transformation

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

A novel method for renormalization in quantum-field theory in curved spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843001 ◽  
Author(s):  
Gabriel Freitas ◽  
Marc Casals
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Kerr Black Hole ◽  
Field Operator ◽  
Massless Scalar ◽  
Energy Tensor ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Curved Spacetime ◽  
Renormalization Method

In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor [Formula: see text] and of the square of the field operator [Formula: see text]. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of [Formula: see text] for a massless scalar field in Bertotti–Robinson spacetime.

Zeta-function regularization of quantum field theory

1990 ◽  
Vol 68 (7-8) ◽  
pp. 620-629 ◽  
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Zeta Function ◽  
Analytic Continuation ◽  
Quantum Field ◽  
Four Dimensions ◽  
Group Functions

Analytic continuation leads to the finite renormalization of a quantum field theory. This is illustrated in a determination of the two loop renormalization group functions for [Formula: see text] in four dimensions.

On the Mathematical Structure of the New-Tamm-Dancoff Procedure

1981 ◽  
Vol 36 (5) ◽  
pp. 421-428
Author(s):  
W. Feist
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Mathematical Structure ◽  
Approximate Determination ◽  
Quantum Field ◽  
C Algebras ◽  
Canonical Anticommutation Relations ◽  
Functional Algebra ◽  
Joint Treatment

Abstract The New Tamm-Dancoff method is a procedure for the approximate determination of differences of eigenvalues in quantum field theory. This procedure can be formulated mathematically in the framework of the theory of C*-algebras, especially in our case by using von Neumann's infinite tensor products. Calculational rules are presented for operators which obey the canonical anticommutation relations. The concept of the CAR tensor product is introduced for the joint treatment of a system algebra and the associated functional algebra, A conjugation is discussed which will be needed for a proof of equivalence in II.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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