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Chapter
Spontaneous Breakdown of Conformal Symmetry
Let us consider a scalar field φ(x) in a Minkowski space. Suppose that along with a conformally in variant vacuum % MathType!MTEF!2!1!+- % fea...
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Chapter
Approximate Methods of Calculating Critical Indices
Conformal symmetry is one of the principles underlying the modern phase transition theory. In this chapter we solve the problem of an approximate computation of critical indices by means of conformal theory me...
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Chapter
Contribution of Electromagnetic and Gravitational Interactions into the General Solution of Ward Identities
The conformal partner of the current is the vector field A μ (x) with dimension % MathType!MTEF!2!1!+-% feaagCar...
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Chapter
Conformal Invariance in Gauge Theories
Let A μ be a gauge field in a 4-dimensional Euclidean space with values in the algebra of the gauge group G. Let us consider the tensor field
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Chapter
Global Conformal Symmetry and Hilbert Space
This chapter has two goals: 1. To obtain general expressions for conformally invariant Wightman functions and Green functions; 2. To study the structure of a Hilbert space of conformally invariant field theory.
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Chapter
Ward Identities
Let φ(x) be a scalar field in Minkowski space. Consider its variations under the action of a group G, which is meant to represent either the space-time transformations group (Poincaré or conformal) or the interna...
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Chapter
Dynamical Sector of the Hilbert Space
As shown in section 5 of the Chapter II, the Hilbert space M of the conformal theory represents a direct sum of subspaces % MathType!MTEF!2!1!...
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Chapter
Goals and Perspectives
The hypothesis that the fundamental laws in Nature have the scale and conformal symmetries has been very attractive to many physicists. The idea is interesting by the fact that the conformal symmetry is the hi...
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Chapter
Special Features of Conformal Transformation of Current, Energy-Momentum Tensor and Gauge Fields
In this Chapter we consider the conformal QED in four dimensional space. The dimensions of potential and current
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Chapter
Euclidean Formulation of the Conformal Theory
A conformal group of Euclidean space is locally isomorphic to the SO(D + 1, l) group. All its irreducible representations are classified by the values of Casimir operators, which have the same formal expressions ...
