Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

In the present paper we discuss the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields based on sedeonic space-time operators and sedeonic wave functions.     

Unified Free Quantum Fields for Massive and for Massless Particles

For any mass m ≧ 0 and arbitrary spin, free relativistic quantum fields are constructed using the same formulas for m > 0 and for m = 0. The transformation properties of these fields under P, C, T and some questions concerning super-selection rules are discussed.     

Massive Gauge Fields and the Planck Scale

No Heading The present work is devoted to massive gauge fields in special relativity with two fundamental constants- the velocity of light, and the Planck length, so called doubly special relativity (DSR). The two invariant scales are accounted for by properly modified boost parameters. Within above framework we construct the vector potential as the (1/2, 0) (0, 1/2) direct product, build the associated field strength tensor together with the Dirac spinors and use them to calculate various observables as functions of the Planck length.     

Interaction Between Massive and Massless Gravitons by Perturbing Topological Field Theory

We test the Wu gauge theory of gravity with massive gravitons in the perturbing topological field theory framework.We show that the computation of the correlation function between massive and massless gravitons is reported up to 4-loop and appears to be unaffected by radiative correction.This result ensures the stability of the linking number between massive and massless gravitons with respect to the local perturbation,a result with potential wider applications in cosmology.     

Relating Thomas-Whitehead Projective Connections by a Gauge Transformation

Thomas-Whitehead projective connections, or TW-connections, are torsionfree linear connections, satisfying certain properties, on a naturally defined principal R-bundle over a manifold. The name credits T. Y. Thomas and J. H. C. Whitehead, who originally studied these connections in the 1920's and 1930's. Three equivalence classes of TW-connections will be considered. This leads to a necessary and sufficient condition for TW-connections to be related by a gauge transformation; namely, they induce the same projective structure on the base manifold, have identical Ricci tensor, and induce the identity element in the one-dimensional de Rham cohomology vector space of the base manifold. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Sharpened Nuclearity Condition for Massless Fields

A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the momentum transfer of local operators in this model.     

Hertz Potentials and Asymptotic Properties of Massless Fields

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.     

Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.     

Effective Gauge Theories of Composite W,Z and Massless Fermions

We have attempted to identify the circumstances under which a weakly coupled massive gauge theory such as the standard Glashow-Salam-Weinberg model, can emerge as a low energy effective Lagrangian of an ASF preon gauge theory. This involves many issues including the interplay between global and local symmetries and sum rules connecting long and short distance physics. The article puts together these issues and demonstrates that ASF preon models can be very tight and predictive frameworks. We make a systematic search of a minimal extension of the standard electro-weak theory, which could emerge as a low energy effective Lagrangian of an ASF preon gauge theory, in which the left-right symmetry is spontaneously broken by vacuum condensation.     

Kontsevich Deformation Quantization and Flat Connections

In Torossian (J Lie Theory 12(2):597–616, 2002), the second author used the Kontsevich deformation quantization technique to define a natural connection ω _n on the compactified configuration spaces [`(C)]_n,0{\overline{C}_{n,0}} of n points on the upper half-plane. Connections ω _n take values in the Lie algebra of derivations of the free Lie algebra with n generators. In this paper, we show that ω _n is flat.     

Periodicity of Y-Systems and Flat Connections

We give a proof of the periodicity of Zamolodchikov’s Y-system in the AxA case using an interpretation of the system as a condition of flatness of a certain graph connection. In our approach, the periodicity property appears as an identity among representations of a matrix as products of two-diagonal matrices.     

Gauge Fields with Generic Singularities

Let Mbe an n-dimensional manifold equipped with an Abelian Yang–Mills field with connection form . We consider an external potential function Vand examine the existence and regularity of the vortex lines of the form +Vdtwhich define the motion of a particle weakly coupled to the Yang–Mills field on M. These curves are smooth unless the curvature form d is singular and in this paper we treat this singular case from a generic aspect. The problem reduces to the division properties for smooth functions and differential forms, the development of which constitutes the main part of the work presented here.     

Massless Fields on Dirac Six-Cone and De Sitter Ambient Space

We have proceeded to obtain manifestly conformally invariant (CI) equations for thinkable graviton fields in de Sitter (dS) space-time. The tensor fields are originally considered in 4+2 dimensional conformal space or Dirac’s six-cone and then project to dS space which is embedded in 4+1 dimensional ambient space. It will be shown that, by projecting these tensor fields there exists a correspondence between the massless fields on the cone and dS space. Also, we have shown that for rank-2 tensor field the divergenceless condition, which is necessary when we attempt to correspond the tensor field with the unitary irreducible representations (UIRs) of dS group, is not really a condition at all, it is a consequence of ambient space property. Due to the combined occurrences of corresponding fields and divergenceless property, the appropriate CI field equations have obtained in a fairly simple way and without imposing any extra condition.     

Generalized Forms, Connections, and Gauge Theories

Generalized differential forms of type N = 2, and flat generalized connections are used to describe the SO(p, q) form of Cartan's structure equations for metric geometries, source-free Yang-Mills fields, and the Einstein–Yang-Mills equations in four dimensions. Maxwell's equations for type N = 2 forms are also constructed.     

Translation Gauge Fields and Space-Time Dislocations

Gauge fields of Poincaré translations define particular nongravitation structure on a space-time, which can be treated as sui generis space-time dislocations. Their source is the canonical energy-momentum tensor of matter, and these dislocations can introduce some corrections to standard values of gravitation effects, e. g. the Yukawa type corrections to the Newtonian gravitation potential.     

Nonrelativistic Wave Equations with Gauge Fields

We illustrate a metric formulation of Galilean invariance by constructing wave equations with gauge fields. It consists of expressing nonrelativistic equations in a covariant form, but with a five-dimensional Riemannian manifold. First we use the tensorial expressions of electromagnetism to obtain the two Galilean limits of electromagnetism found previously by Le Bellac and Lévy-Leblond. Then we examine the nonrelativistic version of the linear Dirac wave equation. With an Abelian gauge field we find, in a weak field approximation, the Pauli equation as well as the spin—orbit interaction and a part reminiscent of the Darwin term. We also propose a generalized model involving the interaction of the Dirac field with a non-Abelian gauge field; the SU(2) Hamiltonian is given as an example.     

Chaotic Quantization of Classical Gauge Fields

We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and calculate Planck's constant from quantities defined in the underlying classical gauge theory.     

Supersymmetric U(1) Gauge Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of U(1) gauge field in supcrsymmctric U(1) gauge theory is discussed.The modelhas the strict local U(1) gauge symmetry and supersymmetry.Because we introduce two vector superfields simultaneously,the model contains a massive U(1) gauge field as well as a massless U(1) gauge field.