Showing papers on "Explicit symmetry breaking published in 1973"

Perturbative Calculations of Symmetry Breaking

Abstract: The one-loop contributions to fermion and pseudo-Goldstone masses are calculated for the general class of renormalizable guage theories. It is shown explicitly that when the masses are subject to any type of zeroth-order symmetry. relation for all values of the parameters in the Lagrangian, the divergences in the one-loop corrections to these symmetry relations cancel. The finite parts of these corrections are evaluated and discussed. Other topics considered include the connection of this work with that of Coleman and E. Weinberg, the constraints obeyed by scalar coupling constants, and the path-integral derivation of the Feynman rules for general renormalizable gauge theories.

Spontaneous Symmetry Breaking Without Scalar Mesons

Abstract: By combining the ideas of Nambu in his study of superconductivity and of Johnson, Baker, and Willey in their approach to electrodynamics we construct a gauge theory of spontaneous symmetry breaking which is free of elementary spin-zero fields. The theory contains two fermions and two vector mesons, one of which acquires a mass via the Higgs mechanism. A formula for this vector-meson mass is derived which becomes exact, and nonzero, in the limit as the strength of interaction is appropriately scaled to zero. The vacuum energy is also discussed.

Group theory for matrix isolated molecules in static crystal fields

Abstract: The group theory is solved for molecules of any symmetry matrix isolated at a site in a crystal field of any symmetry. As the potential barrier to rotation of the molecule relative to the host crystal is raised, certain symmetry operations become decreasingly ``feasible'' in the sense of Longuet‐Higgins. Using correlation methods the symmetry species of the rotational states are determined from the free rotation limit to any of the librational limits. Examples of linear, symmetric, and spherical rotors are given. From the symmetry of states and the dipole and polarizability tensors, selection rules are applied to predict spectra in the infrared and Raman effect.

Perturbation theory for projected states

Abstract: For quantum systems with a symmetry it is often convenient to start from a simple soluble model lacking the symmetry, and restore the symmetry by projection. If this is done for all eigenstates of the model system, one obtains an overcomplete set of basis functions, which is not suitable for standard perturbation theory. The paper develops a method by which one can do perturbation theory in this situation. The method is illustrated by application to the problem of the centre-of-mass motion of a nucleus, the symmetry being the translational and Galileo invariance.

Goldstone Bosons as Bound States in the Quark-Gluon Model

Abstract: We examine the implications of a Nambu-Goldstone realization of chiral symmetry in the quark-gluon model. The context of this examination is that of a renormalizable, finite theory, so eigenvalue conditions are assumed to be satisfied. We discuss the solutions to the Schwinger-Dyson gap equation for the fermion self-energy $\ensuremath{\Sigma}({p}^{2})$ that exhibit spontaneous breaking of the vacuum symmetry. In the leading-order Bethe-Salpeter approximation the boundary conditions to the homogeneous, linear integral equations stipulate the vacuum symmetry. It is shown how the Goldstone bosons emerge as bound states, as suggested by Nambu and Jona-Lasinio. We also examine the Goldstone alternative in the Bethe-Salpeter equation for fermion-fermion scattering. Explicit symmetry breaking is introduced by additional Abelian vector gluons coupling to hypercharge and isospin besides baryon number. The eigenvalue condition for the fine-structure constant is consequently model-dependent but takes a simple form. We also consider the influence of explicit symmetry breaking on the ground-state mesons and indicate how the solutions to the eigenvalue problem regulate the structure of symmetry breaking.

Harmonic oscillator pattern arising from an algebraic approach to chiral symmetry.

Abstract: SummaryIn a previous work we proposed a saturation scheme for theSU3⊗SU3 chiral algebra within an infinite set ofSU6⊗O3 states. A mixing operator was introduced which transforms the axial charges of theSU6 solution into the physical ones,Qi5. Here we saturate the Weinberg equation for the (mass)2 operator [Q5+, [Q5+,m2]]=0, between meson states, in a perturbative approach. The generatorZ of the mixing operators, for which formerly only the transformation properties underSU6×O3 were given, is now completely established asZ=(W×M)z, whereW is theW-spin operator andM is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)2 operator, the lowest term consists of two pieces, the harmonic-oscillator energy and a spin-orbit coupling of the form (−1)L+1(L·S+1/2). The resulting (mass)2 consists of families of equispaced linearly rising trajectories.RiassuntoLo schema di saturazione dell'algebra chiraleSU3⊗SU3 in un insieme infinito di stati diSU6⊗O3 introdotto in un precedente lavoro viene qui completamente definito imponendo le equazioni di Weinberg per l'operatore di massa [Q5+, [Q5+,m2]]=0. Il generatore della trasformazione delle cariche assiali diSU6 in quelle fisiche,Z, è univocamente determinato:Z=(W×M)z doveW è ilW-spin eM l'operatore di posizione dell'oscillatore armonico statico. All'ordine più basso dello sviluppo perturbativo l'operatore di massa consta di due parti: l'energia dell'oscillatore e in termini di spin orbita (−1)L+1(L·S+1/2). Lo spettro è costituito da sei famiglie di traiettorie lineari equispaziate.РезюмеВ предыдущей работе мы предложили схему насыщения дляSU3⊗SU3 чиральной алгебы внутри бесконечной системыSU6⊗O3 состояний. Вводится оператор смешивания, который преобразует аксиальные заряды решенияSU6 в физические зарядыQi5. Здесь мы насьщаем уравнение Вейнберга для оператора квадрата массы [Q5+, [Q5+,m2]]=0, между мезонными состояниями, в подходе теории возмущений. ГенераторZ операторов смешивания, для которых формально заданы только трансформационные свойства относительноSU6×O3, теперь полностью определен в видеZ=(W×M)z гдеW естьW спиновый оператор иM есть координата трехмерного гармонического осциллятора. В разложении теории возмущений оператора квадрата массы низший член состоит из двух частей, энергии осциллятора и спин-орбитальной связи вида (−1)L+1(L·S+1/2). Результирующий квадрат массы состоит из семейств равноотстоящих линейно возрастающих траекторий.

Can All Hadronic Symmetry Breaking Be Due to Weak Interactions

Abstract: We define, in very general terms, a class of theories in which it is possible for all symmetries such as SU(3) and SU(3) @SU(3) to be exact if one turns off all couplings of leptons and hadrons; but nevertheless, one can have ten to twenty percent violations of these symmetries coming about as a direct consequence of extremely weak lepton-hadron couplings. A framework is proposed for discussing these schemes which is independent of specific Lagrangian models and so leaves open the question of whether or not the Goldstone bosons appearing in these schemes are elementary or composite. For pedagogical purposes the last section of this paper is devoted to a brief discussion of a simple Lagrangian model having the various properties set out in our general scheme. (Submitted to The Physical Review) * Supported by the U. S. Atomic Energy Commission.

Is there spontaneous symmetry breaking in gauge theories with the higgs-kibble mechanism?

Abstract: It is argued that gauge theories with the Higgs-Kibble mechanism do not involve the spontaneous breaking of physical symmetries. The relationships between masses and coupling constants, usually considered a manifestation of the remnant of the symmetry, can be obtained, at least in the Abelian-Higgs model, directly from renormalizability and unitarity requirements.

Chiral dynamics as zero-slope limit of the dual pion model

Abstract: It is shown that in taking a particular zero-slope limit (α′→0,m π 2 =finite), the dual pion model reduces to a nonlinear σ-model with (1/2, 1/2) symmetry breaking in the tree approximation.

Stochastic symmetry breaking of time reversal invariance

Abstract: An equation for the time evolution of the density matrix for a nonrelativistic quantum mechanical system is presented. It involves a Hamiltonian which contains a stochastic contribution. Before stochastic averaging is performed, it is shown that the density matrix equation is time reversal invariant, whereas after stochastic averaging is performed, it is shown that the averaged density matrix equation is not time reversal invariant.

A double perturbation theory for molecular complexes

Abstract: Consideration is given to the problem of interactions between molecular systems (magnetic couplings being neglected) by highlighting the fact that the main difficulty of a perturbation theory that takes into account the exchange effects, resides in the differentiated symmetry of the unperturbed state and of the state of interaction (at an overlap other than zero). This difficulty has been overcome by choosing for the Schrodinger equation of the interacting systems a particular representation on the set of unperturbed functions and by reversing the symmetry properties onto the operators. This will lead to a new equation no longer presenting any difficulties for the symmetry interconnection. This equation is used for a double perturbational expansion both in Coulomb and in exchange terms, thus obtaining general perturbation equations. Explicit solutions are provided (up to the second total order) which are briefly discussed.

Broken conformal symmetry. I. The hadron spectrum

Abstract: The breaking of the asymptotic conformal symmetry of strong interactions is investigated. It is assumed that the symmetry is broken by the nonvanishing vacuum expectation value of a scalar field. The first-order symmetry-breaking term in the two-point function is completely determined by the conformally invariant limit of the theory. The model predicts families of almost linear Regge trajectories. It is predicted that the ratio of total widths to masses of resonances is —approximately—a universal constant. Comparison with baryon resonances shows reasonably good agreement with the prediction.

Full use of symmetry in maximum‐determinant rule

Abstract: The properties of Hilbert space and group theory are used to point out the fact that the m-dimensional Laplace-Gauss law for m unknown structure factors, involving two Karle-Hauptman determinants, Δm+ 1 and Dm, can take into account full symmetry information for any space group. It is shown that the ratio (Δm+ 1/Dm) is equal to a sum of ratios of Goedkoop determinants.