6 added 77 characters in body edited Oct 5 '18 at 14:58 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which isan effective theory of spinless fields, which serves as the prototype of the Higgs potential--but don't think Higgs just yet!). The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type (broken dynamically or by a Higgs potential, which might be a summary model thereof), the analogs of the above Goldstone boson degrees of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry,symmetry; but the previous bullet item reminds you you may know nothing about it and enjoy SSB in globally symmetric systems. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!). The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type (broken dynamically or by a Higgs potential, which might be a summary model thereof), the analogs of the above Goldstone boson degrees of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (an effective theory of spinless fields, which serves as the prototype of the Higgs potential--but don't think Higgs just yet!). The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type (broken dynamically or by a Higgs potential, which might be a summary model thereof), the analogs of the above Goldstone boson degrees of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry; but the previous bullet item reminds you you may know nothing about it and enjoy SSB in globally symmetric systems. 5 oops! superconductivity is Higgs phenomenon. edited Oct 4 '18 at 18:57 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!), or the Landau-Ginsburg action in superconductivity, the mother of all SSB phenomena. The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type, (broken dynamically or due toby a Higgs potential (which, which might be a summary model thereof), the analogs of the above Goldstone boson degressdegrees of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!), or the Landau-Ginsburg action in superconductivity, the mother of all SSB phenomena. The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type, dynamically or due to a Higgs potential (which might be a summary model thereof), the Goldstone boson degress of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!). The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type (broken dynamically or by a Higgs potential, which might be a summary model thereof), the analogs of the above Goldstone boson degrees of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. 4 avoiding recondite logical shoals edited Oct 4 '18 at 13:32 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!), or the Landau-Ginsburg action in superconductivity, the mother of all SSB phenomena. The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, upongauging the global SSB systems of the above type, dynamicaldynamically or due to a Higgs potential (which might be a summary model thereof), the Goldstone boson degress of freedom are reconfigured ininto the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!), or the Landau-Ginsburg action in superconductivity, the mother of all SSB phenomena. The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, upon SSB, dynamical or due to a Higgs potential (which might be a summary model thereof), the Goldstone boson degress of freedom are reconfigured in the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. You've made a perfect hash of basically two related by distinct concepts, even though most of your sources are sounder than your summary of them. It is actually unclear what you are asking for. A good book would help, and a perusal of the dozens of relevant questions on this site. I think you should suspend consideration of SSB for the time being; and first appreciate the difference between global and local (gauge) symmetries. Only then segue to SSB. Here is a road map. For global symmetries, such as chiral symmetry in QCD, dynamical strong interaction mechanisms lead to its SSB ("hiding"), producing Goldstone bosons (~ the pions and pseudoscalar mesons), necessarily as per the eponymous theorem. You may further summarize the effects of this dynamical mechanism through the $$\sigma$$-model (which is the prototype of the Higgs potential--but don't think Higgs just yet!), or the Landau-Ginsburg action in superconductivity, the mother of all SSB phenomena. The vacuum of such theories is made degenerate and more interesting, and the symmetry manifests itself in subtler, less visible, ways. For local (gauged) symmetries, gauging the global SSB systems of the above type, dynamically or due to a Higgs potential (which might be a summary model thereof), the Goldstone boson degress of freedom are reconfigured into the gauge bosons of such theories and provide new polarization states to these ("fattened up") gauge bosons. Again, the manifestations of the symmetry are all over, and they are collectively dubbed the "Higgs mechanism", useful in the Weak Interactions. You cannot have this mechanism without SSB of the respective global symmetry, but the previous bullet item reminds you you may know nothing about it and enjoy SSB. 3 finessing the narrow statement. edited Oct 4 '18 at 2:33 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges 2 added 8 characters in body edited Oct 3 '18 at 15:59 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges 1 answered Oct 3 '18 at 15:03 Cosmas Zachos 19.3k22 gold badges4242 silver badges141141 bronze badges