New Curved Spacetime Dirac Equations - On the Anomalous Gyromagnetic Ratio

I propose three new curved spacetime versions of the Dirac Equation. These equations have been developed mainly to try and account in a natural way for the observed anomalous gyromagnetic ratio of Fermions. The derived equations suggest that particles including the Electron which is thought to be a point particle do have a finite spatial size which is the reason for the observed anomalous gyromagnetic ratio. A serendipitous result of the theory, is that, two of the equation exhibits an asymmetry in their positive and negative energy solutions the first suggestion of which is clear that a solution to the problem as to why the Electron and Muon - despite their acute similarities - exhibit an asymmetry in their mass is possible. The Mourn is often thought as an Electron in a higher energy state. Another of the consequences of three equations emanating from the asymmetric serendipity of the energy solutions of two of these equations, is that, an explanation as to why Leptons exhibit a three stage mass hierarchy is possible.Comment: 8 pages, errors corrected, final form of the paper and no further changes to be made. Accepted in the Foundations of Physics Journa

Gauge invariant Lagrangian for non-Abelian tensor gauge fields of fourth rank

Using generalized field strength tensors for non-Abelian tensor gauge fields one can explicitly construct all possible Lorentz invariant quadratic forms for rank-4 non-Abelian tensor gauge fields and demonstrate that there exist only two linear combinations of them which form a gauge invariant Lagrangian. Together with the previous construction of independent gauge invariant forms for rank-2 and rank-3 tensor gauge fields this construction proves the uniqueness of early proposed general Lagrangian up to rank-4 tensor fields. Expression for the coefficients of the general Lagrangian is presented in a compact form.Comment: 27 pages, LaTex fil

Area-preserving Structure and Anomalies in 1+1-dimensional Quantum Gravity

We investigate the gauge-independent Hamiltonian formulation and the anomalous Ward identities of a matter-induced 1+1-dimensional gravity theory invariant under Weyl transformations and area-preserving diffeomorphisms, and compare the results to the ones for the conventional diffeomorphism-invariant theory. We find that, in spite of several technical differences encountered in the analysis, the two theories are essentially equivalent.Comment: 9 pages, LaTe

Nonlinear QED and Physical Lorentz Invariance

The spontaneous breakdown of 4-dimensional Lorentz invariance in the framework of QED with the nonlinear vector potential constraint A_{\mu}^{2}=M^{2}(where M is a proposed scale of the Lorentz violation) is shown to manifest itself only as some noncovariant gauge choice in the otherwise gauge invariant (and Lorentz invariant) electromagnetic theory. All the contributions to the photon-photon, photon-fermion and fermion-fermion interactions violating the physical Lorentz invariance happen to be exactly cancelled with each other in the manner observed by Nambu a long ago for the simplest tree-order diagrams - the fact which we extend now to the one-loop approximation and for both the time-like (M^{2}>0) and space-like (M^{2}<0) Lorentz violation. The way how to reach the physical breaking of the Lorentz invariance in the pure QED case taken in the flat Minkowskian space-time is also discussed in some detail.Comment: 16 pages, 2 Postscript figures to be published in Phys. Rev.

Dirac reduction revisited

The procedure of Dirac reduction of Poisson operators on submanifolds is discussed within a particularly useful special realization of the general Marsden-Ratiu reduction procedure. The Dirac classification of constraints on 'first-class' constraints and 'second-class' constraints is reexamined.Comment: This is a revised version of an article published in J. Nonlinear Math. Phys. vol. 10, No. 4, (2003), 451-46

Recent Results Regarding Affine Quantum Gravity

Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a conventional perturbation analysis. After a brief review of both the scalar field story and the affine quantum gravity program, examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study. Additionally, guided by the projection operator method to deal with quantum constraints, trial reproducing kernels are introduced that satisfy the diffeomorphism constraints. Furthermore, it is argued that the trial reproducing kernels for the diffeomorphism constraints may also satisfy the Hamiltonian constraint as well.Comment: 32 pages, new features in this alternative approach to quantize gravity, minor typos plus an improved argument in Sec. 9 suggested by Karel Kucha

Physical constants and the Gurzadyan-Xue formula for the dark energy

We consider cosmological implications of the formula for the dark energy density derived by Gurzadyan and Xue which predicts a value fitting the observational one. Cosmological models with varying by time physical constants, namely, speed of light and gravitational constant and/or their combinations, are considered. In one of the models, for example, vacuum energy density induces effective negative curvature, while another one has an unusual asymptotic. This analysis also explicitely rises the issue of the meaning and content of physical units and constants in cosmological context.Comment: version corrected to match the one to appear in Modern Physics Letters

On-shell consistency of the Rarita-Schwinger field formulation

We prove that any bilinear coupling of a massive spin-3/2 field can be brought into a gauge invariant form suggested by Pascalutsa by means of a non-linear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit Delta (1232) isobar degrees of freedom are discussed.Comment: 9 pages, 1 figur

Topological insulator and the Dirac equation

We present a general description of topological insulators from the point of view of Dirac equations. The Z_{2} index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic B term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, the Z_{2} index is modified as 1 for mB>0 and 0 for mB<0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a non-trivial one system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation are obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z_{2} index we establish a relation between the Dirac equation and topological insulators.Comment: 9 pages, published versio

General Very Special Relativity is Finsler Geometry

We ask whether Cohen and Glashow's Very Special Relativity model for Lorentz violation might be modified, perhaps by quantum corrections, possibly producing a curved spacetime with a cosmological constant. We show that its symmetry group ISIM(2) does admit a 2-parameter family of continuous deformations, but none of these give rise to non-commutative translations analogous to those of the de Sitter deformation of the Poincar\'e group: spacetime remains flat. Only a 1-parameter family DISIM_b(2) of deformations of SIM(2) is physically acceptable. Since this could arise through quantum corrections, its implications for tests of Lorentz violations via the Cohen-Glashow proposal should be taken into account. The Lorentz-violating point particle action invariant under DISIM_b(2) is of Finsler type, for which the line element is homogeneous of degree 1 in displacements, but anisotropic. We derive DISIM_b(2)-invariant wave equations for particles of spins 0, 1/2 and 1. The experimental bound, $|b|<10^{-26}$, raises the question ``Why is the dimensionless constant $b$ so small in Very Special Relativity?''Comment: 4 pages, minor corrections, references adde