THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY
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Abstract:
An infinite set of conformally invariant solutions of the two-dimensional quantum field theory, possessing a global symmetry Zn is constructed. These solutions can describe the critical behavior of Zn symmetric statistical systems.The conformal invariance and conserved quantities of Mei symmetry for Mechanico-Electrical systems were studied.On the basis of Lagrange-Maxwell equation of this system,conformal invariance of Mei symmetry was obtained and conditions that the conformal invariance should satisfy were deduced.And their determining equations were then given.The relationship between conformal invariance and Noether symmetry,Lie symmetry,and Mei symmetry were discussed,and the corresponding conserved quantities were obtained.Finally,an example was given to illustrate the application of the result.
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Abstract The present chapter is an introductory account of the basic concepts and important consequences of conformal symmetry, i.e. the invariance under local scale transformations, in field theories characterizing critical behaviour. The goal is to catalogue universality classes as a list of possible values of critical exponents and to find restrictions on the functional forms of correlation functions, which satisfy conformal Ward identities. From a mathematics standpoint, conformal symmetry applies to continuum theories, and therefore its obvious application to critical phenomena is formulated in the language of field theory. The energy-momentum tensor plays a fundamental role in defining the conformal generators that satisfy the Virasoro algebra, and any conformal field theory is characterized by the central charge a number that is important to classify critical field theories. One of the most remarkable applications of conformal field theory is found in the analysis of finite-size effects.
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