Showing papers on "Explicit symmetry breaking published in 1970"

Weak Interactions with Lepton-Hadron Symmetry

Abstract: We propose a model of weak interactions in which the currents are constructed out of four basic quark fields and interact with a charged massive vector boson. We show, to all orders in perturbation theory, that the leading divergences do not violate any strong-interaction symmetry and the next to the leading divergences respect all observed weak-interaction selection rules. The model features a remarkable symmetry between leptons and quarks. The extension of our model to a complete Yang-Mills theory is discussed.

Renormalizable models with simple symmetry breaking. i. symmetry breaking by a source term.

Abstract: If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.

Charges and generators of symmetry transformations in quantum field theory

Abstract: Within the Wightman approach to quantum field theory, we review and clarify the properties of formal charges, defined as space integrals for the fourth component of a local current. The conditions for a formal charge to determine an operator (generator) are discussed, in connection with the well-known theorems of Goldstone and of Coleman. The symmetry transformations generated by this operator---given its existence---are also studied in some detail. For generators in a scattering theory, we prove their additivity and thus provide a simple way to characterize them from their matrix elements between one-particle states. This characterization allows an immediate construction of the unitary operators implementing the symmetry transformations, and implies that all internal symmetry groups are necessarily compact. We also indicate how to construct interacting fields having definite internal quantum numbers. The present status of the proof of Noether's theorem and of its converse is discussed in the light of the rather delicate properties of formal charges.

Asymptotic locality and the structure of local internal symmetries

Abstract: Symmetries are investigated from the local viewpoint. Using the Haag-Ruelle construction, the action of a local internal symmetry on the asymptotic states is determined. A condition of “asymptotic locality” is derived and used to show that the symmetry acts linearly and locally on the asymptotic fields. Within a field theoretical framework it is shown that the internal symmetry must commute with the Poincare group. The general structure of an internal symmetry is determined. The uniqueness of the representation of the Poincare group is discussed, and a simple example of an infinite component field is given to indicate what occurs when there are infinitely degenerate particle multiplets.

Is the Group R4 an Approximate Symmetry for Many‐Electron Theory?

Abstract: The 4‐dimensional rotation group R4 is used to analyze the structure of the (2s + 2p)N shell and to determine the relevance, if any, of the R4 group as an approximate symmetry group for many‐electron theory. It is found that while the R4 symmetrized states of the (2s + 2p)N complex approximately diagonalize the Coulomb energy matrix for interactions within the complex, the inclusion of the inner 1s2 shell effects leads to a large symmetry violating term, which invalidates the R4 group as an approximate symmetry for many‐electron theory.

Interpretation of the Symmetry of the Clebsch‐Gordan Coefficients Discovered by Regge

Abstract: An interpretation is proposed for the intriguing symmetry of the Clebsch‐Gordan coefficients discovered in 1958 by Regge. The interpretation is based on the observation that, in the reduction of the Kronecker product of two irreducible representations of an SU(2) group, there appears in a natural way another SU(2) group, which is almost independent of the original one. The Regge symmetry is interpreted as the symmetry under the interchange of these two SU(2) groups. In more picturesque language, the Regge symmetry is the symmetry under the interchange of the ``two‐ness'' of the two angular momenta being added with the ``two‐ness'' of SU(2). It follows from this interpretation that a symmetry of the same nature is present in the generalized Clebsch‐Gordan coefficient that appears in the reduction of the Kronecker product of n (and not two, except when n = 2) irreducible representations of SU(n).

Generalized Group‐Theoretical Analysis of Spontaneous Symmetry Breaking

Abstract: A group‐theoretical analysis of spontaneous symmetry breaking is carried out in an extension of Glashow's work. A general theorem is proved which is then used to give several interesting results. Apart from a rederivation of Glashow's result, we are able to show, among other things, the following: If a hadronic triplet exists in nature which is nontrivially coupled to the rest of the hadrons, then octet enhancement immediately follows independently of any dynamical detail; in models containing the vector nonet, φ ‐ ω mixing can, in principle, occur as a particular form of spontaneous symmetry breaking in the octet pattern; and if octet enhancement holds, the very accurate mass formula mφ2+mω2=2mk2* is established without recourse to any dynamical detail. Under the same general assumption, a further relation is found relating the mass of the nonet with the mixing angle, which is 4mk2*−3(cos2θmφ2+sin2θmω2)−mρ2=0.

Exchange symmetry of many-particle state functions.

Abstract: A formal operator definition of indistinguishability of identical particles alternative to permutation invariance of configuration probabilities is presented. The exchange-symmetry properties of many-particle wave functions are shown to follow simply and directly from the new definition.