Dynamical properties of antisymmetric tensor fields

The physical degrees of freedom of free actions involving antisymmetric tensor fields are analyzed. While massless spin zero as well as massive vector particles can be represented by such fields, we show that massive scalars cannot, and that some actions have no dynamical content at all. We also show that electromagnetic (unlike gravitational) interactions cannot be included consistently in the spin zero case. Supersymmetric extension of the tensor formulation is given, and it is shown that, in analogous antisymmetric tensor-spinor incarnations, fermions cannot couple consistently to gravity.     

Geometric fermions

We study the Kähler-Dirac equation which linearizes the laplacian on the space of antisymmetric tensor fields. In flat space-time it is equivalent to the Dirac equation with internal symmetry and on the lattice it reproduces Susskind fermions. The KD equation in curved space-time differs from the Dirac equation by coupling the gravitational field to the internal symmetry generators. This new way of treating fermionic degrees of freedom may lead to a solution of the generation puzzle but is in conflict with the equivalence principle and with Lorentz invariance on the Planck-mass scale.     

Open bosonic strings in general background fields

We discuss the renormalization properties of the 2 dim. field theory describing an open bosonic string in the background fields corresponding to its massless excitations. The relevant β-functions are calculated for gravitational, antisymmetric tensor and Yang-Mills background on 1-loop level, for pure Yang-Mills background an 2-loop level and in the Abelian case up to 3 loops. We find a renormalization scheme dependence starting at 2 loop order. Putting β to zero yields the equation of motion for the non-linear electrodynamics of Fradkin and Tseytlin.     

Neutralization of the cosmological constant by membrane creation

The quantum creation of closed membranes by totally antisymmetric tensor and gravitational fields is considered in arbitrary space-time dimension. The creation event is described by instanton tunneling. As membranes are produced, the energy density associated with the antisymmetric tensor fielld decreases, reducing the effective value of the cosmological constant. For a wide range of parameters and initial conditions, this process will naturally stop as soon as the cosmological constant is near zero, even if the energy remaining in the antisymmetric tensor field is large. Among the instantons obtained, some are interpreted as representing a topology change, in which an open space spontaneously compactifies; however, the quantum probability for these processes vanishes.     

Antisymmetric tensor fields in a generalized Randall–Sundrum scenario

Bulk antisymmetric tensor fields of different ranks have been studied in the context of a generalized Randall–Sundrum model with a non-vanishing induced cosmological constant on the visible brane. It is shown that instead of the usual exponential suppression of the couplings of the zero modes of these bulk fields with the brane fermions in the original Randall–Sundrum model, here the couplings are proportional to the brane cosmological constant. Thus in an era of large cosmological constant these fields have significant role in physical phenomena because of their enhanced couplings with the visible brane fermions.     

A study of fermions coupled to gauge and gravitational fields on a cylinder

Fermions on a cylinder coupled to background gravitation and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. We are able to show that the gauge coupling constant is constrained to a value of 1/N where N is an integer. Furthermore, in direct analogy with a Yang-Mills theory a new gravitational theory is introduced which couples to the fermions by promoting the coadjoint vector of the diffeomorphism sector to a dynamical variable. The classical dynamics of this theory are examined by displaying its symplectic structure and showing that it is equivalent to a one-dimensional system.     

TheB (3) field as a link between gravitation and electromagnetism in the vacuum

The emergence of theB ⁽³⁾ field in vacuo has shown that electromagnetism is non-Abelian and similar in structure to gravitation. In this paper the Christoffel symbol used in general relativity is developed for electromagnetism in curvilinear coordinates: The former becomes describable as the antisymmetric part of the gravitational Ricci tensor. Therefore gravitation and electromagnetism are respectively the symmetric and antisymmetric parts of thesame Ricci tensor within a proportionality factor. Both fields are obtained from the Riemann curvature tensor, both are expressions of curvature in spacetime.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

Unification of gravitation and electromagnetism with B(3)

The experimentally supported existence of the Evans Vigier field.B ⁽³⁾,in vacuo implies that the gravitational and electromagnetic fields can be unified within the same Ricci tensor, being respectively its symmetric and antisymmetric components in vacuo. The fundamental equations of motion of vacuum electromagnetism are developed in this framework.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

Strings and Antisymmetric Tensor Fields

The string model described by antisymmetric tensor fields which in many respects are analogous to spinors, is considered. So new possibilities in constructing the unified theory of physical interaction is appeared.     

Introduction of a second-rank antisymmetric tensor into null aesthetic field theory

We are able to incorporate an antisymmetric second-rank tensor into null aesthetic field theory. There are some changes in the solutions due to the introduction of this antisymmetric second-rank tensor, which we discuss. We are not able to find an acceptable bounded particle system in four space-time dimensions.     

On the new representation of the antisymmetric tensor gauge field

A formalism is presented which provides a framework for analysis of the abelian gauge theory of a second-rank anti-symmetric tensor in terms of the mutually dual auxiliary fields. This new formalism illustrates how the different gauge fixing conditions are related to the different field representations exhibiting the rich dynamical features of the antisymmetric tensor gauge fields. The derivation relies upon an analogy with the simpler case of the two-dimensional Maxwell field.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

On a Lagrangian formulation of gravitoelectromagnetism

We examine a Lagrangian formulation of gravity based on an approach analogous to electromagnetism, called Gravitoelectromagnetism (GEM). The gravitational analogue of the electromagnetic field tensor is a three-index tensor, \({\mathcal {F}_{\mu\nu\lambda}}\), defined in terms of a two-index gravitoelectromagnetic potential, \({\mathcal {A}_{\mu\nu}}\). The energy-momentum tensor is derived and is symmetric. We construct a Lagrangian which allows us to describe interactions between fermions, photons and gravitons. We calculate transition amplitudes of various processes involving gravitons: gravitational Møller scattering, gravitational Compton scattering, and the graviton photoproduction.     

Gravitational two-body problem—A source theory viewpoint

An analysis of the semirelativistic gravitational two-body problem based on Schwinger's source theory is given. Our treatment is purely classical but nongeometrical. Only the large distance behavior of the gravitational stress tensor is seen to be relevant for order G² contributions. For a gravitational stress tensor that has a pure Newtonian form, only the traceless choice is seen to be consistent with Einstein's theory. We find results in agreement with the earlier results of Einstein, Infeld, and Hoffmann, and Barker and O'Connell for spin-2 graviton exchanges between Dirac particles, and with Börner, Ehlers, and Rudolph for spin precession in theories with arbitrary post-Newtonian parameter γ. The source approach clearly displays the analogy between gravitational interactions and classical electrodynamics. We also discuss the general relationship between the periastron advance and spin-precession frequencies for a class of gravitation theories. Brief estimates of the various spin-precession effects are given for the Hulse-Taylor pulsar.     

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory.