Spontaneous symmetry breaking in annealed and quenched gauge field models

The structure of annealed and quenched models with localU(1) gauge invariance is studied in terms of the Helmholtz free energy. The first non-trivial, or one-loop, account of fluctuations in the annealed model suggests that spontaneous symmetry breaking occurs in two and three dimensions, through a first-order phase transition. Within the same approximation scheme, the quenched model displays a continuous phase transition. A more complete account of the fluctuations in the annealed model changes the nature of the transition to a continuous one, whereas spontaneous symmetry breaking is then absent with quenched disorder.     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

Spontaneous symmetry breaking in massless field theories: Dimensional transmutation and gauge independence

In a reformulation of the Coleman and Weinberg program, we study the parametrization of the spontaneous symmetry breaking solutions of massless field theories. Our analysis is based on a full use of the concept of the dimensional transmutation, namely the parametrization in terms of the independent invariants of the underlying renormalization group. This invariant parametrization provides a convenient setting for the operator interpretation in a given Fock space and is shown to be a powerful tool in studying general aspects of the theory beyond the one-loop approximation. In particular, the gauge independence of the physical matrix elements in the spontaneously broken solution of massless scalar electrodynamics is demonstrated to all orders in perturbation theory.     

Spontaneous symmetry breaking in local gauge quantum field theory; the Higgs mechanism

Spontaneous symmetry breakings in indefinite metric quantum field theories are analyzed and a generalization of the Goldstone theorem is proved. The case of local gauge quantum field theories is discussed in detail and a characterization is given of the occurrence of the Higgs mechanism versus the Goldstone mechanism. The Higgs phenomenon is explained on general grounds without the introduction of the so-called Higgs fields. The basic property is the relation between the local internal symmetry group and the local group of gauge transformations of the second kind. Spontaneous symmetry breaking ofc-number gauge transformations of the second kind is shown to always occur if there are charged local fields. The implications about the absence of mass gap in the Wightman functions and the occurrence of massless particles associated with the unbroken generators in the Higgs phenomenon are discussed.     

Spontaneous symmetry breaking and fermion chirality in higher-dimensional gauge theory

The number of chiral fermions may change in the course of spontaneous symmetry breaking. We discuss solutions of a six-dimensional Einstein-Yang-Mills theory based on SO(12). In the resulting effective four-dimensional theory they can be interpreted as spontaneous breaking of a gauge group SO(10) to $\text{H}\text{=}\text{SU}\text{(3)}{}_{\mathrm{<mtext>C</mtext>}}\text{×}\text{SU}\text{(2)}{}_{\mathrm{<mtext>L</mtext>}}\text{×}\text{U}\text{(1)}{}_{\mathrm{<mtext>R</mtext>}}\text{×}\text{U}\text{(10)}{}_{\mathrm{B?L}}$. For all solutions, the fermions which are chiral with respect to $\text{H}$ form standard generations. However, the number of generations for the solutions with broken SO(10) may be different compared to the symmetric solutions. All solutions considered here exhibit a local generation group SU(2)_G × U(1)_G. For the solutions with broken SO(10) symmetry, the leptons and quarks within one generation transform differently with respect to SU(2)_G × U(1)_G. Spontaneous symmetry breaking also modifies the SO(10) relations among Yukawa couplings. All this has important consequences for possible fermion mass relations obtained from higher-dimensional theories.     

Spontaneous symmetry breaking in Reggeon field theory

We consider a Reggeon field theory when the bare or input Regge intercept α_O is greater than one. This corresponds to a negative mass squared term in conventional field theory and allows for a spontaneous symmetry break-down. A theory with Regge intercept at one emerges, restoring the Froissart bound by t-channel considerations alone. In our elementary example the resulting bare trajectory is nearly of the square root variety familiar from s-channel eikonalization of models which violate the Froissart bound.     

Spontaneous symmetry breaking of affine field theory

It is possible to construct non-Abelian field theories by gauging Kac-Moody algebras. Here we discuss the spontaneous symmetry breaking of such theories via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra.     

Spontaneous symmetry breaking of Slavnov symmetry A restriction on the gauge condition

It is shown that the condition of vanishing vacuum expectation value of the gauge operator, using a gauge-fixing term quadratic in this operator, does not necessarily follow from the Slavnov identity, due to a possible spontaneous breakdown of the Slavnov symmetry. For a consistent renormalization such a condition may have to be imposed order by order in perturbation theory, depending on the choice of the gauge. This restriction on non-singular gauges is particularly relevant for the discussion of the spontaneously broken realizations of the gauge symmetry.     

Spontaneous symmetry breaking in cosmological models with rotation

We study the possibility of spontaneously broken gauge symmetry in the theory of a charged massive or massless scalar field for cosmological models of the Gödel and Ozsvath-Schücking types. We consider the effect of spontaneous symmetry breaking in the construction of a new cosmological solution with rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 22–26, February, 1989.The author thanks the participants of the seminars of Prof. A. A. Grib and Prof. D. D. Ivanenko for discussions of the results.     

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.     

A note on gauge symmetry breaking

We show that the breaking of Abelian gauge symmetry implies the existence of dipole singularities in the correlation functions of the (Abelian) Higgs model. We also show that the noninvariance of the Wightman functions does not preclude the implementability of the global gauge symmetry. An explicit example of gauge symmetry breaking (Ferrari's model) is discussed.     

Spontaneous breaking of electric-magnetic charge symmetry in local quantum field theory

It is shown that in local quantum field theory with electric and magnetic currents, duality transformations are always spontaneously broken. Possible implications are discussed leading to the screening of magnetic charge and the failure of the cluster property as in two-dimensional quantum electrodynamics.     

Spontaneous symmetry breaking in massless field theories,finite temperature and criticality

We study the behaviour at finite temperature of massless field theories exhibiting spontaneously broken solutions. We establish the occurence of a phase transition of the first kind at some critical point T_c which can be calculated to any finite order in perturbation theory. Similarly, perturbative methods can be used for thermodynamic functions in all regions, including the critical region. For the case of a gauge theory, we demonstrate the gauge independence of the critical point, the thermodynamic potentials and the order parameter to all orders of perturbation theory.