Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales

Abstract

We discuss the phase transition in 3+1 dimensional lambda Phi^4 theory from a very physical perspective. The particles of the symmetric phase (`phions') interact via a hard-core repulsion and an induced, long-range -1/r^3 attraction. If the phion mass is sufficiently small, the lowest-energy state is not the `empty' state with no phions, but is a state with a non-zero density of phions Bose-Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with <Phi> neq 0 and its excitations ("phonons" in atomic-physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m^2 passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M_h. This interesting physics coexists with `triviality;' all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio m/M_h, which goes to zero in the continuum limit, can be viewed as a measure of non-locality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.

27 pages plus 2 files of figures

Cited by in corpus (34)

• Constraints on the Size of the Smallest Triggering Earthquake from the ETAS Model, Baath's Law, and Observed Aftershock Sequences
• Stock Market Speculation: Spontaneous Symmetry Breaking of Economic Valuation
• The Lehman Brothers Effect and Bankruptcy Cascades
• Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction
• A variational study of bound states in the Higgs model
• The classical ether-drift experiments: a modern re-interpretation
• Kurt Symanzik - a stable fixed point beyond triviality
• Light Higgs bosons from a strongly interacting Higgs sector
• Vacuum condensates and `ether-drift' experiments
• Comparison of perturbative RG theory with lattice data for the 4d Ising model
• Cosmic Microwave Background and the issue of a fundamental preferred frame
• Emergent gravity and ether-drift experiments
• Ultraweak excitations of the quantum vacuum as physical models of gravity
• Spontaneous symmetry breaking and the $p\to 0$ limit
• A weak, attractive, long-range force in Higgs condensates
• Renormalization-Group flow for the field strength in scalar self-interacting theories
• The mass scales of the Higgs field
• The CMB, preferred reference system and dragging of light in the earth frame
• An alternative heavy Higgs mass limit
• On the Chiral Phase Transition in the Linear Sigma Model
• Experimental signals for a second resonance of the Higgs field
• Precision tests with a new class of dedicated ether-drift experiments
• Path Integral Treatment of Singular Problems and Bound States: Quantum Mechanics
• Do 1/r potentials require massless particles ?
• Indications on the Higgs boson mass from lattice simulations
• The long-range interaction in massless (lambda Phi^4)_4 theory
• On the low-energy spectrum of spontaneously broken Φ^4 theories
• Higgs boson origin from a gauge symmetric theory of massive composite particles and massless $W^{\pm }$ and $Z^0$ bosons at the TeV scale
• Long-wavelength excitations of Higgs condensates
• Hydrodynamics of the Vacuum
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints
• Quantum Non-Locality and the CMB: what Experiments say
• Dynamics of the Scalar Condensate in thermal 4D self-interacting Scalar Field Theory on the Lattice
• Zero temperature lattice Weinberg - Salam model for the values of the cutoff $\Lambda \sim 1$ TeV