arXiv:hep-ph/9911218v2 26 Apr 2000 HIP-1999-65/TH Quantum Magnetic Collapse M. Chaichian a,b , S.S. Masood c,e , C. Montonen b , A. P´ erez Mart´ ınez d , H. P´ erez Rojas a,b,e a High Energy Division, Department of Physics, University of Helsinki, b Helsinki Institute of Physics, P.O. Box 9, FIN-00014 University of Helsinki, Finland c Physics Department, Quaid-i-Azam University, Islamabad, Pakistan d ICIMAF, Calle E No. 309, 10400 La Habana, Cuba e International Centre for Theoretical Physics P.O. Box 586, Strada Costiera 11, 34100 Trieste, Italy Abstract We study the thermodynamics of degenerate electron and charged vector boson gases in very intense magnetic fields. In degenerate conditions of the electron gas, the pressure transverse to the magnetic field B may vanish, leading to a transverse collapse. For W -bosons an instability arises because the magnetization diverges at the critical field B c = M 2 W /e. If the magnetic field is self-consistently maintained, the maximum value it can take is of the order of 2B c /3, but in any case the system becomes unstable and collapses. Large magnetic fields can be generated due to gravitational and rotational effects in stel- lar objects like supernovas and neutron stars, i.e., magnetic fields of order 10 20 G and larger have been suggested to exist in the cores of neutron stars [1]. The standard electroweak the- ory establishes a limit on the magnetic field, the critical upper bound for stable vacua being B c = M 2 W /e ≃ 1.06 · 10 24 G, coming from the W ± ground state energy ǫ 0q =  M 2 W − eB, which is imaginary for B>B c . Fields of order B c may have been created at the electroweak phase transition (see [3], [2]). The galactic and intergalactic magnetic fields can be consid- ered as relics of such huge magnetic fields in the early Universe [4]- [8]. In astrophysics, also the critical field B c ′ = m 2 e /e ≃ 4.41 · 10 13 G is relevant. Nielsen, Olesen and Ambjørn [9], [10] showed that the vacuum possesses the properties of a ferromagnet or an antiscreening superconductor for B ∼ B c . It thus seems relevant to study the electroweak medium in a strong magnetic field of the order of the critical magnetic fields. The implications of these results for astroparticle physics and cosmology are expected to be interesting. As in preceding papers (Refs. [11], [12]), we only consider the first generation of leptons and quarks for the sake of simplicity. Here we shall calculate the 1