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By V A Miransky
The phenomenon of dynamical symmetry breaking (Dsb) in quantum box concept is mentioned in an in depth and complete means. The deep connection among this phenomenon in condensed subject physics and particle physics is emphasised. The realizations of Dsb in such real looking theories as quantum chromodynamics and electroweak idea are thought of. concerns in detail attached with Dsb akin to serious phenomenona and potent lagrangian method also are mentioned.
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19) T he physical meaning of this property is clear: ciusterization implies the absence of instantaneous long-range correlations in the system, so that the dynamics in two distant spatially-separated regions are independent. 21) in the infinite volume. However, since (Nl cp(x) IN + I) #- we see that G(2)(x) does not vanish as 0, (N + llcpt(O)IN) #- x2 --; 00. 22) 0 , (We note that in the infinite volume, ho th the state IN}and the state IN + I) have the same density n, therefore we must take i"l,o account the contribution of the IN + I}-state).
9. DYNAMICAL U(I) GAUGE SYMMETRY BREAKING IN THE BCS MODEL Dynamical symmetry breaking is a special case of spontaneous symmetry breaking in which the condensate (order parameter) is given by the vacuum average of a composite (and not elementary) operator. 57). 98) =e -2iO (0 I1jJp (x )1jJa( X )ID) in which case />,tId is necessarily zero. Let us consider the structure of the BCS ground state. 71). B. (p), &(p), iJ. 7D) . $ Symmetry Breaking in Conden&ed Matter 35 However there is a crucial difference between the dynamics of these two cases.
41) E(k)::=uk (and not E '" k 2 ) as k -+ 0. 26), one finds that when the velocity v is smaller than u, superfluidity occurs in the system. Let us consider the content of the vacua IB) in the terms of the initial particles connected with the operators ak, at. 42) In particular the density nk = Nk/V goes to zero as V no = No/V is finite at V = 00. -+ 00. 4, we find the explicit representation of the vacua IB): 10) = exp( - N/2)exp(N~/2eiOa6) II(1- L~)1/4. rc with I ~q . (l. (2. 10) ). m Field Theories vacua transform as Ie) ~ uo, le) = Ie + e').