scholarly journals Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking

2006 ◽  
Vol 39 (25) ◽  
pp. 8205-8219 ◽  
Author(s):  
Florian Schütz ◽  
Peter Kopietz
Keyword(s):  
Renormalization Group ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Vacuum Expectation ◽  
Expectation Values ◽  
Functional Renormalization Group

Gauge hierarchies for chiral SU(N) × SU(N) groups

1976 ◽  
Vol 54 (16) ◽  
pp. 1660-1663 ◽  
Author(s):  
Shalom Eliezer
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Text Representation ◽  
Algebraic Equations ◽  
Expectation Values ◽  
Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

scholarly journals UA(1) SYMMETRY BREAKING AND THE SCALAR SECTOR OF QCD

2001 ◽  
Vol 16 (17) ◽  
pp. 3011-3024 ◽  
Author(s):  
M. NAPSUCIALE ◽  
S. RODRIGUEZ
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Vacuum Expectation ◽  
Spontaneous Breaking ◽  
Expectation Values ◽  
Qualitative And Quantitative ◽  
Quantitative Level ◽  
Pseudoscalar Mesons ◽  
Scalar Sector

It is shown that most of the unusual properties of the lowest lying scalar (and pseudoscalar) mesons can be understood, at the qualitative and quantitative level, on the basis of the breakdown of the UA(1) symmetry coupled to the vacuum expectation values of scalars by the spontaneous breaking of chiral symmetry.

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