scholarly journals Double-scaling limit of a broken symmetry quantum field theory in dimensions D<2

2001 ◽  
Vol 42 (5) ◽  
pp. 1960 ◽  
Author(s):  
Carl M. Bender ◽  
Stefan Boettcher ◽  
H. F. Jones ◽  
Peter N. Meisinger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scaling Limit ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Double Scaling Limit

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals Broken Symmetry and Yang–Mills Theory

2014 ◽  
Vol 03 (01) ◽  
pp. 54-67 ◽  
Author(s):  
François Englert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Statistical Physics ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Yang Mills

From its inception in statistical physics to its role in the construction and in the development of the asymmetric Yang–Mills phase in quantum field theory, the notion of spontaneous broken symmetry permeates contemporary physics. This is reviewed with particular emphasis on the conceptual issues.

scholarly journals Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.

1998 ◽  
Vol 10 (06) ◽  
pp. 775-800 ◽  
Author(s):  
D. Buchholz ◽  
R. Verch
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Relativistic Quantum ◽  
Free Field ◽  
Scaling Limit ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Spatial Dimensions ◽  
Local Observables

The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article this method is applied to the simple example of massive free field theory in s=1,2 and 3 spatial dimensions. Not quite unexpectedly, one obtains for s=2,3 in the scaling (short distance) limit the algebra of local observables in massless free field theory. The case s=1 offers, however, some surprises. There the algebra of observables acquires in the scaling limit a non-trivial center and describes charged physical states satisfying Gauss' law. The latter result is of relevance for the interpretation of the Schwinger model at short distances and illustrates the conceptual and computational virtues of the method.

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".  

Sign in / Sign up

Export Citation Format

Share Document