Spontaneous Lorentz violation: the case of infrared QED

It is by now clear that the infrared sector of quantum electrodynamics (QED) has an intriguingly complex structure. Based on earlier pioneering work on this subject, two of us recently proposed a simple modification of QED by constructing a generalization of the U(1) charge group of QED to the ``Sky'' group incorporating the well-known spontaneous Lorentz violation due to infrared photons, but still compatible in particular with locality (Balachandran and Vaidya, Eur Phys J Plus 128:118, 2013). It was shown that the ``Sky'' group is generated by the algebra of angle-dependent charges and a study of its superselection sectors has revealed a manifest description of spontaneous breaking of the Lorentz symmetry. We further elaborate this approach here and investigate in some detail the properties of charged particles dressed by the infrared photons. We find that Lorentz violation due to soft photons may be manifestly codified in an angle-dependent fermion mass, modifying therefore the fermion dispersion relations. The fact that the masses of the charged particles are not Lorentz invariant affects their spin content, and time dilation formulas for decays should also get corrections.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Role of orbital symmetry in transition metal promoted ring opening reactions of methylenecyclopropanes and cyclobutenes

Transition metals catalyse a variety of organic reactions, of which the ring opening of strained ring organic molecules generated a lot of interest. Theoreticians predicted a metal orbital catalysed pathway, which involved concerted bond breaking and bond forming. On the other hand experimentalists were able to show that the reaction was not proceeding through a concerted pathway by intercepting the intermediates involved. There remained, however, two ring systems methylenecyclopropanes and cyclobutenes—whose reactions with metal complexes seemed to be of a concerted nature. An analysis of the reactions of different metal complexes with these ring systems and the theoretical predictions provide a rationale for understanding these reactions.

Restoration of symmetry by radiative corrections

It is shown using an explicit model that radiative corrections can restore the symmetry of a system which may appear to be broken at the classical level. This is the reverse of the phenomenon demonstrated by Coleman and Weinberg. Our model is different from theirs, but the techniques are the same. The calculations are done up to the two-loop level and it is shown that the two-loop contribution is much smaller than the one-loop contribution, indicating good convergence of the loop expansion.

Mechanistic Aspects of Shape Selection and Symmetry Breaking during Nanostructure Growth by Wet Chemical Methods

The control of shapes of nanocrystals is crucial for using them as building blocks for various applications. In this paper, we present a critical overview of the issues involved in shape-controlled synthesis of nanostructures. In particular, we focus on the mechanisms by which anisotropic structures of high-symmetry materials (fcc crystals, for instance) could be realized. Such structures require a symmetry-breaking mechanism to be operative that typically leads to selection of one of the facets/directions for growth over all the other symmetry-equivalent crystallographic facets. We show how this selection could arise for the growth of one-dimensional structures leading to ultrafine metal nanowires and for the case of two-dimensional nanostructures where the layer-by-layer growth takes place at low driving forces leading to plate-shaped structures. We illustrate morphology diagrams to predict the formation of two-dimensional structures during wet chemical synthesis. We show the generality of the method by extending it to predict the growth of plate-shaped inorganics produced by a precipitation reaction. Finally, we present the growth of crystals under high driving forces that can lead to the formation of porous structures with large surface areas.

Sterochemical studies on cyclic peptides-VIII. Conformational analysis of hydrogen bonded cyclohexaglycyl molecule with a centre of inversion symmetry

A study on the conformational aspects of cyclo-hexaglycyl having inversion symmetry has been made. The cyclic backbone has been assumed to have two internal 4→1 types of NH... O hydrogen bonds. This molecule has been found to take up two types of conformations designated asA* andB* having nearly the same energy values. The theoretical conformations have been compared with the conformations of cyclohexaglycyl hemihydrate observed in the crystal structure. Two molecules with an approximate inversion symmetry are close to the conformation of the typeB* and two other molecules with exact inversino symmetry correspond nearly to the typesB* andA*. comparison with the theoretically possible conformations of cyclohexaglycyl molecule with 2-fold symmetry has been made. The preference of inversion symmetry and preferred ranges ofψ for glycyl molecules is discussed.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

Possible high-temperature superconducting state with a d plus id pairing symmetry in doped graphene

Motivated by a suggestion in our earlier work [G. Baskaran, Phys. Rev. B 65, 212505 (2002)], we study electron correlation driven superconductivity in doped graphene where on-site correlations are believed to be of intermediate strength. Using an extensive variational Monte Carlo study of the repulsive Hubbard model and a correlated ground state wave function, we show that doped graphene supports a superconducting ground state with a d+id pairing symmetry. We estimate superconductivity reaching room temperatures at an optimal doping of about 15%-20%. Our work suggests that correlations can stabilize superconductivity even in systems with intermediate coupling.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Symmetry and shape issues in nanostructure growth

Symmetry plays a key role in dictating the equilibrium morphology of crystals. However, several growth morphologies that deviate from the point group symmetry are routinely observed under several different growth conditions. In this article, we present a summary of symmetry-breaking mechanisms that are operative for crystals grown from the vapour phase as well as those formed as a result of wet chemical synthesis. This understanding is crucial for rationalizing the variety of morphologies observed during nanocrystal synthesis and also providesa rational framework for the synthesis of anisotropic nanostructures.

X-ray diffraction from single Al6CuLi3 grains showing five-fold symmetry

We present here the detailed results of X-ray diffraction from single quasicrystals of Al6CuLi3. X-ray precession photographs taken down the two-, three- and five-fold axes along with rotation and zero-level Weissenberg photographs are shown. Preliminary analysis of the diffraction data rules out the twin hypothesis.

Symmetry preservation during radiation damage

An examination of radiation-damage processes consequent to high-energy irradiation in certain ammonium salts studied using ESR of free radical together with the structural information available from neutron diffraction studies shows that, other factors being equal/nearly equal, symmetry-related bonds are preserved in preference to those unrelated to one another by any symmetry.