Kalb–Ramond fields and the CMBR

Cosmological implications on the polarization of the cosmic microwave background radiation, of a Kalb–Ramond field interacting with gauge fields and gravity as dictated by quantum consistency of heterotic string theory are surveyed. A parity violating augmentation going beyond the dictates of string theory is shown to lead to possible appearance of a B mode generated in the cosmic microwave background (CMB) in the post-last scattering epoch. This generation of the B mode of CMB appears to be dramatic when the augmentation is embedded within a Randall–Sundrum braneworld scenario of the first kind.     

A comment on Kerr–CFT and Wald entropy

We point out that the entropies of black holes in general diffeomorphism invariant theories, computed using the Kerr–CFT correspondence and the Wald formula (as implemented in the entropy function formalism), need not always agree. A simple way to illustrate this is to consider Einstein–Gauss–Bonnet gravity in four dimensions, where the Gauss–Bonnet term is topological. This means that the central charge of Kerr–CFT computed in the Barnich–Brandt–Compere formalism remains the same as in Einstein gravity, while the entropy computed using the entropy function gives a universal correction proportional to the Gauss–Bonnet coupling. We argue that at least in this example, the Kerr–CFT result is the physically reasonable one. The resolution to this discrepancy might lie in a better understanding of boundary terms.     

Minimal Coupling of the Kalb–Ramond Field to a Scalar Field

We study the direct interaction of an antisymmetric Kalb–Ramond field with a scalar particle derived from a gauge principle. The method outlined in this paper to define a covariant derivative is applied to a simple model leading to a linear coupling between the fields. Although no conserved Noether charge exists, a conserved topological current comes out from the antisymmetry properties of the Kalb–Ramond field. Some interesting features of this current are pointed out. Possible applications of our results to cosmology and to the theory of three-dimensional Josephson junction arrays are envisaged.     

On a Unified Theory of Generalized Branes Coupled to Gauge Fields,Including the Gravitational and Kalb–Ramond Fields

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates and associated coordinate frame fields {} extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space.     

A comment on Bonnor–Steadman closed timelike curves

The existence and stability closed timelike curves in a Bonnor–Ward spacetime without torsion line singularities is shown by exhibiting particular examples.     

A reply to “a comment on generalized electromagnetism and Dirac algebra”

Issues raised by W. A. Rodrigues, Jr. are discussed.1. This is not a new result; see,e.g., Rohrlich.⁽³⁾ 2. A typographical error in Eq. (77) is corrected here: The productj A in the right-hand parentheses was erroneously transcribed in Ref. (2) as A.3. I define electromagnetic fieldF = A to be that generated by electric charges and the magnetoelectric fieldG = M to be that generated by magnetic monopoles:F F +₅ G. 4. Rodrigues, on the other hand, takes the position that the importance of the Lagrangian formulation should be downgraded if not discarded altogether: ... it is redundant to look for Lagrangians.⁽¹⁾ 5. In fact, he reformulates it using the language of differential forms.6. It is interesting to observe that this bilinear form has the additional virtue of being appropriate for dealing with the monopolecharge parity question, which was pointed out long ago.⁽¹⁴⁾ 7. In fact, even mathematics looks to Nature for its authority.⁽¹⁶⁾ There is evidence that Rodrigues does not understand this concept.⁽¹⁷⁾     

A lattice Maxwell system with discrete space–time symmetry and local energy–momentum conservation

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space–time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy–momentum conservation law corresponding to the discrete space–time symmetry. A lattice model that respects all local conservation laws and geometric structures is as good as and probably more preferable than standard models on continuous space–time. It can also be viewed as an effective algorithm for the governing differential equations on continuous space–time.     

Anisotropic power-law inflation of the five dimensional scalar–vector and scalar-Kalb–Ramond model

We will study the cosmological implications of the five dimensional scalar–vector and scalar-Kalb–Ramond model. In particular, a new set of Bianchi type I power-law analytic solution will be obtained for this model. The cosmic no-hair conjecture can be shown to break down in the presence of the scalar–vector and scalar-Kalb–Ramond couplings. The effect of the Kalb–Ramond field in the presence of the power-law solution will be shown explicitly. We will also show that the presence of a phantom field does, however, destabilize the corresponding Bianchi type I power-law inflationary solutions.     

Large-scale magnetic fields from inflation due to a <Emphasis Type="Italic">CPT</Emphasis>-even Chern–Simons-like term with Kalb–Ramond and scalar fields

We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the CPT-even dimension-six Chern–Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb–Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that magnetic fields on 1 Mpc scale with the field strength of ∼10⁻⁹ G at the present time can be induced.     

A comment on “critique of home and sengupta's derivation of a Bell inequality”

We clarify some aspects of our derivation of a Bell-type inequality, in response to a paper by Elby.The following comments refer to Andrew Elby's discussion note immediately following our present paper.(a) We wish to stress that physical distinction between NC and LC is particularly important in the case of local realist theories violating NC for any single system but satisfying LC for any correlated many-component system. Arguments given by Elby do not rule out a reasonable theory violating NC but obeying LC. Therefore, a physically meaningful possibility exists that while Bell's inequality derived from NC is violated for a single system, the inequality derived from LC is satisfied for correlated and spatially separated (non-interacting) systems. It is precisely this possibility which was explored by HS in deriving Bell's inequality from NC.(b) Since Elby's formulation of locality condition necessarily involves a relativistic constraint at the level of individual measurements, it is pointless to discuss its compatibility with predictions derived from non-relativistic quantum mechanics, which is well known to allow superluminal communication by mechanisms such as wavepacket travel or spread. Recently this aspect has been discussed in depth by P. Ghose and D. Home,Phys. Rev. A 43, 6382 (1991). It needs to be stressed that our formulation of LC is in line with the separability condition articulated by Einstein in different contexts; see, for example,J. Franklin Inst. 221, 349 (1936), reprinted inIdeas and Opinions (Crown, New York, 1954), pp. 290–323.On leave from: Department of Physics, Bose Institute, Calcutta 700009, India.     

Quantum noise in the mirror–field system: A field theoretic approach

We revisit the quantum noise problem in the mirror–field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror’s displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation–dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror.     

A phase field model for vesicle–substrate adhesion

In this paper, a phase field model is developed for vesicle adhesion involving complex substrate and vesicle geometries. The model takes into account an adhesion potential that depends on the distance of vesicle to the substrate. A variational problem is solved in a 3D computational domain by minimizing the contribution of bending elastic energy and the adhesion energy under the constraints of total surface area and volume, described via a phase function. An adaptive finite element method is used to efficiently compute the numerical solutions of the model. The computational results are validated through comparison of several axisymmetric shapes with the sharp-interface ODE solution. Moreover, we compute shapes for non-axisymmetric situations to support the observation that concave substrates favor adhesion.     

Decoupling and reduction in Chern–Simons modified gravity

We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.     

Eisenhart lift in pseudo–Euclidean space and higher rank killing tensors

It is emphasized that the Eisenhart lift applied to integrable systems in pseudo–Euclidean space may result in Ricci–flat metrics of ultrahyperbolic signature which admit higher rank Killing tensors.     

Magnetic properties and reduction characteristics of Fe–Co–B catalysts

Hyperfine Interactions - The effect of the amount of boron on the magnetic properties and the reduction characteristics of Fe–Co–B catalysts have been studied by Thermal Programmed...     

A neutral spinning particle in interaction with a magnetic field and Poschl–Teller potential

The problem of a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a Poschl–Teller potential is considered via path integrals. The calculations are carried out explicitly using an external current source. The problem is then reduced to that of a spinning forced Poschl–Teller oscillator whose spin is coupled to external derivative current sources. The result of the propagator is given as a series. The relative propagator of this forced oscillator is converted to that of an angular momentum via an extension of the dimension. Next, the series is exactly summed by means of a Laplace transformation and the orthonormalization relation of the eigenfunctions of the angular momentum. Received: 29 June 2001 / Published online: 23 November 2001