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The associated conserved current is in .NET
The associated conserved current is Decoding PDF 417 In .NET Framework Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications. Create PDF 417 In Visual Studio .NET Using Barcode creator for VS .NET Control to generate, create PDF417 2d barcode image in Visual Studio .NET applications. j"(x) = o"</>(x) PDF 417 Scanner In .NET Using Barcode recognizer for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Barcode Generator In VS .NET Using Barcode creator for VS .NET Control to generate, create barcode image in Visual Studio .NET applications. (1136) Barcode Reader In .NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. PDF417 Maker In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create PDF 417 image in .NET applications. The vacuum is, of course, not invariant under these transformations. If we substitute </>(x) for A in Eq. (1130) we find (1137) Alternatively, the total "charge" lim Qv(t) PDF417 Maker In Visual Studio .NET Using Barcode encoder for ASP.NET Control to generate, create PDF417 image in ASP.NET applications. PDF 417 Generator In VB.NET Using Barcode creator for .NET framework Control to generate, create PDF417 2d barcode image in Visual Studio .NET applications. V+oo
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v~oo
eiAQv(O) 10) (1140) 1.1.) = lim exp
v~oo
2(2n) d k 3[a(k) e ik ' x
at(k) eik'XJ} 10) = e(J /2)[a(O)a'(O)] (1141) It appears therefore as a coherent superposition of zeroenergy momentum states. To show that <A 1 0) vanishes we have to be more careful in the handling of the infinitevolume limit. It is better to introduce a smooth spatial cutoff, for instance, (1142) The reader can easily verify that
<01 A) = e n (J.V
)'/64 V~oo
(1143) A physically meaningful model exhibiting spontaneous symmetry breaking is based on a set of n coupled scalar fields with a lagrangian f >(ljJ) = i(8ljJ)2 _ /1 ljJ2 _ ~(ljJ2)2 2 4 (1144) QUANTUM FIELD THEORY
<1>2
invariant under an internal O(n) symmetry group. The notation is such that l/J stands for the column vector of these fields and symmetry breaking will occur if the baremass parameter /1 2 is negative. At the classical level the ground state is not described by a zero mean field value due to the fact that the potential /1 A V(l/J) = _l/J2 + _(l/J2 2
(1145) has a minimum for a nonvanishing value of the field (Fig. 115) 1l/JI=v= ( :f
/12)1/2 (1146) To insure the stability of the theory we assume, of course, that large values of l/J are damped, which means A > 0. It appears as if the vacuum is degenerate: every state with Il/J 1 = v is a priori a candidate. However, any choice leads to an inequivalent Hilbert space. Note that such a choice of a groundstate value l/Jv will leave an O(n  1) subgroup unbroken, corresponding to those transformations which act as the identity on l/Jv. To be specific, let us pick a coordinate system in internal space such that l/Jv = <Oll/J 10) has only its nth component nonvanishing, and parametrize the field in terms of a radial displacement p and (n  1) orthogonal rotations as l/J = e t {Iv ( (1147) SYMMETRIES
The ta with 1 :::; a :::; n  1 stand for n  1 generators of the O(n) group acting effectively on the vector lPv. In other words, the Lie algebra of O(n) contains in addition to the O(n  1) generators the n  1 ta's. When expressed in terms of the new dynamical variables p and ~ the lagrangian reads ft' = i(Op)2 + i(O~2  2 + p  4 (v + p)4 (1148) From this we see that the ~ correspond to (n  1) decoupled massless fields, as predicted by Goldstone's theorem. In the previous example, to be studied in more detail in Sec. 114, the groundstate degeneracy is apparent at the classical level. We have learnt, however, in Chap. 9 that quantum corrections can alter the potential, leading to the possibility of vacuum degeneracy as a result of radiative corrections. This appears to be the case for the following model for scalar electrodynamics, as pointed out by Coleman and Weinberg. A complex massless boson field is coupled minimally to an electromagnetic field. The lagrangian is ft' = ft'em
+ i(oqh
 eAcP2
+ i(OcP2 + eAcPr)2  (cPi + cP~)2 (1149) The complex field cP is written in terms of its two real components cPl and cP2. Moreover, the anharmonic coupling constant is denoted A/4! to compare the oneloop computation of the effective potential with the expression given by Eq. (9129) for the lagrangian (1150) which led to the result

