Lattice-dynamical study of the premartensitic state of the Cu-Al-Be alloys

Neutron-scattering techniques have been used to study the premartensitic state of a family of Cu-Al-Be alloys, which transform from the bcc phase to an 18R martensitic structure. We find that the phonon modes of the TA2[110] branch have very low energies with anomalous temperature dependence. A slight anomaly at q=2/3 was observed; this anomaly, however, does not change significantly with temperature. No elastic peaks, related to the martensite structure, were found in the premartensitic state of these alloys. The results are compared with measurements, performed under the same instrumental conditions, on two Cu-Al-Ni and a Cu-Zn-Al martensitic alloy.

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Dimensional reduction and gauge group reduction in Bianchi-type cosmology

In this paper we examine in detail the implementation, with its associated difficulties, of the Killing conditions and gauge fixing into the variational principle formulation of Bianchi-type cosmologies. We address problems raised in the literature concerning the Lagrangian and the Hamiltonian formulations: We prove their equivalence, make clear the role of the homogeneity preserving diffeomorphisms in the phase space approach, and show that the number of physical degrees of freedom is the same in the Hamiltonian and Lagrangian formulations. Residual gauge transformations play an important role in our approach, and we suggest that Poincaré transformations for special relativistic systems can be understood as residual gauge transformations. In the Appendixes, we give the general computation of the equations of motion and the Lagrangian for any Bianchi-type vacuum metric and for spatially homogeneous Maxwell fields in a nondynamical background (with zero currents). We also illustrate our counting of degrees of freedom in an appendix.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Derivation of the gauge-invariant action for open and closed free bosonic string field theories

The gauge-invariant actions for open and closed free bosonic string field theories are obtained from the string field equations in the conformal gauge using the cohomology operations of Banks and Peskin. For the closed-string theory no restrictions are imposed on the gauge parameters.

Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Constraints on additional Z' gauge bosons from a precise measurement of the Z mass

We analyze the constraints on the mass and mixing of a superstring-inspired E6 Z' neutral gauge boson that follow from the recent precise Z mass measurements and show that they depend very sensitively on the assumed value of the W mass and also, to a lesser extent, on the top-quark mass.

Renormalization of gauge-invariant operators and the axial anomaly

The renormalization properties of gauge-invariant composite operators that vanish when the classical equations of motion are used (class II^a operators) and which lead to diagrams where the Adler-Bell-Jackiw anomaly occurs are discussed. It is shown that gauge-invariant operators of this kind do need, in general, nonvanishing gauge-invariant (class I) counterterms.

Gauge-invariant actions from constraint Hamiltonian dynamics

Dirac's constraint Hamiltonian formalism is used to construct a gauge-invariant action for the massive spin-one and -two fields.

Equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories

A geometrical treatment of the path integral for gauge theories with first-class constraints linear in the momenta is performed. The equivalence of reduced, Polyakov, Faddeev-Popov, and Faddeev path-integral quantization of gauge theories is established. In the process of carrying this out we find a modified version of the original Faddeev-Popov formula which is derived under much more general conditions than the usual one. Throughout this paper we emphasize the fact that we only make use of the information contained in the action for the system, and of the natural geometrical structures derived from it.

Interaction of a discrete breather with a lattice junction

We study the scattering of a moving discrete breather (DB) on a junction in a Fermi-Pasta-Ulam chain consisting of two segments with different masses of the particles. We consider four distinct cases: (i) a light-heavy (abrupt) junction in which the DB impinges on the junction from the segment with lighter mass, (ii) a heavy-light junction, (iii) an up mass ramp in which the mass in the heavier segment increases continuously as one moves away from the junction point, and (iv) a down mass ramp. Depending on the mass difference and DB characteristics (frequency and velocity), the DB can either reflect from, or transmit through, or get trapped at the junction or on the ramp. For the heavy-light junction, the DB can even split at the junction into a reflected and a transmitted DB. The latter is found to subsequently split into two or more DBs. For the down mass ramp the DB gets accelerated in several stages, with accompanying radiation (phonons). These results are rationalized by calculating the Peierls-Nabarro barrier for the various cases. We also point out implications of our results in realistic situations such as electron-phonon coupled chains.