The Anti-ferromagnetic Vacuum

The ferromagnetic condensate is a well known device for mass generation in particle physics ever since the seminal work of Nambu and Jona-Lasinio. This condensate is a coherent state of particles with vanishing momentum. We suggest in this talk the use of another type of condensate in Quantum Field Theory which is a coherent state consisting of particles with non-zero momentum. The field operator which has non-homogeneous vacuum expectation value in this vacuum oscillates with the characteristic momentum of the particles of the condensate. Based on the formal similarity with the Neèl state of the antiferromagnetic Ising model this condensate will be called anti-ferromagnetic. The realistic theories of Particle Physics are effective models since we do not know the physics up to infinite energies. Each effective theory has an energy range where it is supposed to be applicable and contains effective interactions due to the particle exchange processes occuring beyond its energy regime. The impact of these effective vertices is usually classified by the AppelquistCarazzone decoupling theorem, which states that the non-renormalizable effective vertices are suppressed by the ratio of the light and the heavy particle mass. This result is usually taken as an indication that the effect of these vertices whose number is uncontrollably large is numerically small and it is enough to take into account the contributions of the heavy particle exchange processes to the renormalizable vertices only as far as the low energy physics is concerned. It is overlooked in this argument that the decoupling theorem is based on