Mass-generation,symmetry breaking and conformal invariance

We present a principle of mass-generation in which conformal invariance is only spontaneously broken. Some examples are given and we speculate about the relation to the Higgs-Kibble mechanism and the renormalizability of such models.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

电荷对称破缺

1930年 ,物理学家海森伯曾认为 ,中子与质子实质上是在质量上具有微小差别的同一种粒子 ,他将两者统称为“核子” .近代的核物理学家赞同这样的观点 ,即在大量的核反应中 ,如果用中子来代替质子时 ,核反应过程将以相同方式继续进行下去 ,反之亦然 .但这种相似性在某些情况下会发生破坏 ,因为它将导致电荷对称破缺 ,简称为CSB .2 0 0 3年 4月 ,在美国费城召开的美国物理学会的会议上 ,有两个实验室分别独立地宣布 ,他们完成了对电荷对称破缺的实验观测 .一个是美国印第安那大学回旋加速器实验室 (IUCF) .IUCF的E .Stephenson教授宣…     

Solvent-induced symmetry breaking

Symmetry breaking can be induced in a number of ways including interactions with a solvent. An example is the triiodide ion which is centrosymmetric in the gas phase. Molecular dynamics simulations of the triiodide ion in solution have been used to investigate the extent of symmetry breaking in a variety of solvents. We find that the triiodide ion loses its symmetry in water, ethanol, and methanol which form hydrogen bonds with the ion. This results in a localization of charge at one end of the ion and breaking of the geometric symmetry. The extent of symmetry breaking increases as the temperature is lowered. Correlation times for interconversion are reported and the energetics of symmetry breaking are presented. Analogies are made with second-order phase transitions.     

Supergravity,the seven-sphere,and spontaneous symmetry breaking

N = 1 supergravity in d = 11 dimensions spontaneously compactifies on S⁷ to an N = 8 supergravity in d = 4 with a local SO(8) × SO(8) invariance, probably enlargeable to SO(8) × SU(8). Apart from group manifolds, S⁷ is the only compact manifold to admit an absolute parallelism. This permits (a) a “squashing” of S⁷ which gives expectation values to the scalar fields and (b) a parallelizing “torsion” which gives expectation values to the pseudoscalars. This correspondence between extrema of the d = 4 effective potential and solutions of the d = 11 field equations provides a Kaluza-Klein origin for the spontaneous breakdown of gauge symmetries, discrete symmetries, and supersymmetries. It also puts a new perspective on the puzzle of the cosmological constant.     

Gravitation and spontaneous symmetry breaking

It is pointed out that the Higgs field may be supplanted by an ordinary Klein-Gordon field conformally coupled to the space-time curvature, and with very small, real, rest mass. Provided there is a bare cosmological constant of order of its square mass, this field can induce spontaneous symmetry breaking with a mass scale that can be as large as the Planck-Wheeler mass, but may be smaller. It can thus play a natural role in grand unified theories. In the theory presented here the physical cosmological constant is small, being of order of the squared mass, and can meet observational constraints without having to be cancelled accurately. The physical gravitational constant differs somewhat from the coupling constant in Einstein's equation, and is temperature dependent in the broken symmetry regime. Symmetry restoration occurs at high temperature.Research supported by the Arnow Chair in Astrophysics.     

Discrete symmetry and GUT breaking

We study the supersymmetric GUT models in which the supersymmetry and GUT gauge symmetry can be broken by a discrete symmetry. First, with the ansatz that there exist discrete symmetries in the branes' neighborhoods, we discuss the general reflection symmetries and GUT breaking on and . In those models, the extra dimensions can be large and the KK states can be set arbitrarily heavy. Second, considering that the extra space manifold is the annulus or the disc , we can define any symmetry and break any 6-dimensional N=2 supersymmetric SU(M) models down to the 4-dimensional N=1 supersymmetric models for the zero modes. In particular, there might exist the interesting scenario on where just a few KK states are light, while the others are relatively heavy. Third, we discuss the complete global discrete symmetries on and study the GUT breaking. Received: 12 February 2002 / Published online: 14 June 2002     

Space-time geometry and symmetry breaking

We look for solutions of the Einstein-Yang-Mills equations in a 4 + D dimensional space-time. We find solutions where the first 4 dimensions are a flat Minkowskian space-time, while the D others are a compact, space-like manifold of small size. Such solutions can be obtained for an arbitrary compact gauge group K and are invariant under a sub-group G of K related to the space-time geometry. This shows that 4 + D dimensional gravity can give a mechanism for the super-strong symmetry breaking needed in grand unified field theories without introducing Higgs scalars.     

Dynamical electroweak symmetry breaking

In theories of dynamical electroweak symmetry breaking, the electroweak interactions are broken to electromagnetism by the vacuum expectation value of a fermion bilinear. These theories may thereby avoid the introduction of fundamental scalar particles, of which we have no examples in nature. In this note, we review the status of experimental searches for the particles predicted in technicolor, topcolor, and related models.     

Quantum measurements,phase transitions,and spontaneous symmetry breaking

It is shown that if quantum measurement results in a phase transition in a detector medium, then due to orthogonality of Fock spaces of different vacuums the final state cannot be distinguished from the mixture. Examples for transitions in ferromagnetic and vapor-liquid systems are considered. A new formalism is proposed in which EPR-Bohm nonlocal correlations are described as spontaneous symmetry breaking of the pair system state.     

Horizontal symmetries,dynamical symmetry breaking and neutrino masses

We study experimental and theoretical constraints which can prevent the introduction of horizontal gauge ssymmetries. To allow for the possibility of dynamical symmetry breaking, we restrict the symmetry breaking interactions to have the quantum numbers of spin-zero bound states of the fermions in the theory. Under these circumstances we find that horizontal interactions, which do not violete any of the present bounds on flavor changing processes, are only allowed if the symmetry breakdown introduces a large Majorana mass for the neutrinos. Some phenomenological consequences of this result are discussed.     

Infrared bounds,phase transitions and continuous symmetry breaking

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (·) ₃ ² quantum field theories and classical, isotropic Heisenberg models in 3 or more dimensions. The central element of the proof is that for fixed ferromagnetic nearest neighbor coupling, the absolutely continuous part of the two point function ink space is bounded by 0(k ^–2). When applicable, our results can be fairly accurate numerically. For example, our lower bounds on the critical temperature in the three dimensional Ising (resp. classical Heisenberg) model agrees with that obtained by high temperature expansions to within 14% (resp. a factor of 9%).Research supported by USNSF under grants GP-38048 and MPS-74-13252A. Sloan Fellow; also in the Department of Physics     

Gluon condensates,chiral symmetry breaking and pion wave-function

We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.     

Dual models and spontaneous symmetry breaking

The question of spontaneous symmetry breaking in dual models is investigated. In the context of a particular model with a conserved “charge”, two different approaches to the problem, spurion emission and the effective potential methods, are developed. A method is described for the calculation of the effective potential, and it is applied to determine the first few terms of the potential.     

Chiral symmetry breaking and perturbative QCD

Exact results are given for the propagators of axial and vector divergences at the two-loop level of dimensionally regularized quantum chromodynamics. We prove that any combination of propagators that vanishes at zero momentum by virtue of Ward identifies is free of subtractions and satisfies a superconvergence relation. Sum rules for other combinations will, however, involve unknown non-perturbative constants.