On the lyman problem

This paper attempts to answer Lyman's question (1990) on the non-uniqueness in defining the 3D measure of the boundary vorticity-creation rate. Firstly, a straightforward analysis of the vorticity equation introduces a definition of a general vorticity flux-density tensor and its ‘effective’ part. The approach is strictly based on classical field theory and is independent of the constitutive structure of continuous medium. Secondly, the fundamental question posed by Lyman dealing with the ambiguity of the 3D measure of the boundary vorticity-creation rate for incompressible flow is discussed. It is shown that the original 3D measure (for an incompressible Newtonian fluid defined by Panton 1984), which is reminiscent of an analogy to Fourier's law, is in its character ‘effective’ and plays a crucial role in the prognostic vorticity transport equation. The alternative 3D measure proposed by Lyman includes, on the other hand, a ‘non-effective’ part, which plays a role in the local determination of the ‘effective’ measure as well as in a certain diagnostic integral boundary condition.     

Conformal invariance and scalar-tensor theories

A new generalisation of Einstein’s theory is proposed which is invariant under conformal mappings. Two scalar fields are introduced in addition to the metric tensor field, so that two special choices of gauge are available for physical interpretation, the ‘Einstein gauge’ and the ‘atomic gauge’. The theory is not unique but contains two adjustable parameters ζ anda. Witha=1 the theory viewed from the atomic gauge is Brans-Dicke theory (ω=−3/2+ζ/4). Any other choice ofa leads to a creation-field theory. In particular the theory given by the choicea=−3 possesses a cosmological solution satisfying Dirac’s ‘large numbers’ hypothesis.     

SU(N) supersymmetry onS 3 × R spacetime

As the whole physical community is celebrating 30 years of supersymmetry, the aim of the present paper is to analyse an 50(3,1) ×SU(N)— gauge invariant supersymmetric model on the Einstein’s universe. Thus, by exploiting the maximalS ³ symmetry, which allows the use of group theoretical techniques, we deal with a (1/2, 1, 3/2)—spin particle system on theS ³ ×R manifold. After we derive the Dirac-Rarita-Schwinger-Yang-Mills-type field equations, we focus on the additional terms that come into theory as a result of the compactness of space and spin coupling to gravity.     

Conformational analysis of allyl halides from the calculation of indirect spin-spin coupling

A theoretical study on the conformation of allyl halides from the calculation of nuclear spin-spin coupling constants by adopting the finite perturbation theory (FPT), is carried out in terms of the self-consistent, semi-empirical INDO (intermediate neglect of differential overlap) approximation of molecular orbital theory. Results of the calculations performed using ‘s’ and ‘p’ valence orbitals alone (‘sp’ basis) at INDO level approximation seem to replicate the experimental trend quite satisfactorily. Despite the overall agreement of the theoretical values with the experimental ones, the uncertainties in the INDO parametrization scheme lead to overestimation of certain coupling constants. The calculations also show that the orientation of the coupled protons with respect to the substituent halogen atom is an important factor to be considered.     

Cosmological models with constant deceleration parameter in Nordtvedt’s theory

Exact solutions of the field equations of Nordtvedt’s theory for spatially flat FRW models with constant deceleration parameter have been obtained. Singular solutions with (i) power-law (ii) exponential expansion have been studied in Nordtvedt’s theory where the coupling parameterω is a function of the scalar fieldφ.     

Generalized Fock spaces,new forms of quantum statistics and their algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ‘infinite’, Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are: new algebras for infinite statistics,q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ‘doubly-infinite’ statistics, many representations of orthostatistics, Hubbard statistics and its variations.     

Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.      

Paracharge phenomenology: systematics of the new hadrons

A systematic semiquantitative account of all aspects of the strong and electromagnetic interactions of all the newly discovered hadronic states (theψ’s, theχ’s, etc.) is presented within the framework of the paracharge scheme. Extensions of ideas familiar from the SU₃ classification scheme to SU₄ are shown to provide an understanding of the new states seen in the decays ofψ (3.1) andψ′ (3.7), including their masses and gross decay characteristics. The decays ofψ (3.1) andψ′ (3.7) themselves are studied in some detail. Since these are of electromagnetic origin in the scheme, their electromagnetic mixing with the resonance at 4.15 GeV (theP-state of the scheme) is important. Once this is taken into account, the resulting picture is in excellent agreement with available data.     

Fifty years of Szigeti’s dielectric theory — A review

During the period 1949–1961 Szigeti published four seminal papers on the dielectric behaviour of crystals. Szigeti’s theory is applicable to isotropic and anisotropic, ionic and covalent crystals with different structures. Szigeti’s theory connects dielectric, spectroscopic and elastic properties. An important outcome of Szigeti’s theory is the concept of the effective ionic charge (s). It is pointed out that s correlates with a number of physical properties and is a measure of ionicity of the interatomic bond. Since Szigeti’s work, several theoretical models have been proposed to account for the fact that s < 1. These models provide an insight into the complex polarization mechanisms in solids. This review summarizes Szigeti’s work and the work that followed; the implications and applications of Szigeti’s theory are discussed. Some new results are also included. Dedicated to the memory of late Prof. P S Narayanan.     

Topos theory and consistent histories: The internal logic of the set of all consistent sets

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some way. However, in this paper the alternative approach is considered in which all consistent sets are kept, leading to a type of ‘many-world-views’ picture of the quantum theory. It is shown that a natural way of handling this situation is to employ the theory of varying sets (presheafs) on the spaceB of all nontrivial Boolean subalgebras of the orthoalgebraUP of history propositions. This approach automatically includes the feature whereby probabilistic predictions are meaningful only in the context of a consistent set of history propositions. More strikingly, it leads to a picture in which the ‘truth values’ or ‘semantic values’ of such contextual predictions are not just two-valued (i.e., true and false) but instead lie in a larger logical algebra—a Heyting algebra—whose structure is determined by the spaceB of Boolean subalgebras ofUP. This topos-theoretic structure thereby gives a coherent mathematical framework in which to understand the internal logic of the many-world-views picture that arises naturally in the approach to quantum theory based on the ideas of consistent histories.     

From two mesons and (V-A) weak currents to the standard model of quark and lepton interactions

This retrospective paper traces the conceptual evolution of two theories in which the author was involved—the two-meson theory (with H A Bethe) in 1947 and the universal (V-A) theory of weak interactions (with E C G Sudarshan) in 1957—into the present-day standard model of particle interactions. Part 1 is entitled ‘From the pion to QCD and pseudo-Goldstone bosons” and Part 2 “From the muon and neutrino to QFD and chiral anomalies’. Adapted from two lectures delivered at the University of Rochester in October, 1987.     

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell’s theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell’s theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.     

Magnetic and electric birefringence in the isotropic phase of nematic liquid crystals

A theory is developed of the anomalous magnetic and electric birefringence in the isotropic phase of nematic liquid crystals taking into account orientational correlations between neighbouring molecules. Use is made of a modification of Bethe’s method due to Krieger and James, and the properties of the system are derived in terms of a single parameter, viz., the two-particle interaction constant. The expressions for the magnetic and electric birefringence are similar in form to those given by the phenomenological model of de Gennes. Theoretical curves forp-azoxyanisole reproduce the trends in the observed data. A calculation of the nematic-isotropic transition point confirms that this treatment is an improvement over the mean field approximation in describing pre-transition phenomena in the isotropic phase.     

On the classical solution of SO(3) gauge theory and ’t Hooft-Polyakov monopole

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.     

Bianchi Type-III String Cosmological Models

Bianchi type III space time is considered in the presence of cosmic strings in Einstein’s general theory of relativity. Exact cosmological models are presented with the help of relation C=B ⁿ between metric coefficients C and B. Some physical properties of the model in each cases are discussed.     

Are the Laws of Physics Inevitable?

Social constructionists believe that experimental evidence plays a minimal role in the production of scientific knowledge, while rationalists such as myself believe that experimental evidence is crucial in it. As one historical example in support of the rationalist position, I trace in some detail the theoretical and experimental research that led to our understanding of beta decay, from Enrico Fermi’s pioneering theory of 1934 to George Sudarshan and Robert Marshak’s and Richard Feynman and Murray Gell-Mann’s suggestion in 1957 and 1958, respectively, of the V–A theory of weak interactions. This is not a history of an unbroken string of successes, but one that includes incorrect experimental results, incorrect experiment-theory comparisons, and faulty theoretical analyses. Nevertheless, we shall see that the constraints that Nature imposed made the V–A theory an almost inevitable outcome of this theoretical and experimental research.     

Stability of naked singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary C²-mass functionM(r, v) and a C¹-functionh(r, v) (through the corresponding C¹-metric functionν(t, r)), there exist infinitely many choices of energy distribution functionb(r) such that the ’true’ initial data(M, h(r,v)) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a ’big’ subset of the true initial data set, their occurrence is not generic. The terms ’stability’ and ’genericity’ are appropriately defined following the theory of dynamical systems. The particular case of radial pressurep _r (r) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.     

Exotic spectra, wavefunctions and transport in incommensurate lattices

We present numerical results on a range of related issues for a number of incommensurate TMB’s, each of which shows a metal-insulator type transition as a binding-to-hopping ratio is made to increase through some limiting value. These supplement a series of similar results on a couple of 1D lattices in a number of recent works (see below). A brief review pertaining to spectral properties and wavefunctions in incommensurate lattices is followed by results on the above TBM’s relating to an interesting correlation between the gross features of wavefunctions and the energies arranged in a particular sequence termed thelattice-ordered sequence, and also between the lattice-ordered energies and the on-site potentials. We present a qualitative explanation of these correlations on the basis of perturbation theory. Basic results on dynamics of wavepackets in relation to spectral characteristics of incommensurate TBM’s are also reviewed. Features of lattice-ordered energies and wavefunctions for the TBM’s under study are used in the framework of the so-called Maryland construction, leading to a qualitative prediction of criteria for recurrent and non-recurrent wavepacket dynamics in these lattices, and these predictions are checked against numerical iterations of the relevant ‘quantum maps’. Closely related to the dynamics of wavepackets are the transport properties of these lattices. Results are available to indicate that the unusual spectral characteristics of pseudorandom lattices lead to novel features in transport properties of these systems. In this context, low temperature a.c conductivity in these lattices is a good probe for the spectral characteristics and wavefunctions. However, not much is known about the a.c conductivity, excepting a set of early results pertaining to the low frequency regime, principally because of the fact that the a.c conductivity depends on global characteristics of the spectrum and the entire set of wavefunctions. We present a simple model whereby the gross structure of variation of the a.c conductivity with frequency can be obtained from a knowledge of the spectrum alone for the set of TMB’s under consideration. Numerical computations show that despite its simplicity, the model leads to results in good agreement with those from the Kubo-Greenwood formula for a.c conductivity.     

On the interference absorption of X-rays in crystals with weak deformations

The problem of Borrmann absorption (anomalous absorption) of X-rays in weakly deformed crystals is considered on the basis of Takagi’s approach to the dynamical theory. Using wave function considerations, the attenuation of rays is represented by exp(−σl) where the attenuation factor σ includes a parameter of the lattice deformation field. The possibility of cases σ = 0 and even σ < 0 is discussed.