Nonexistence of the Lanczos potential for the Riemann tensor in higher dimensions

The existing refutal, in four-dimensional spacetimes, of the conjecture that the Lanczos tensor can be used as a potential for the Riemann tensor, is derived in a much simpler manner which is valid for dimension n 4 and any signature.     

Generalized Lanczos method for systematic optimization of tensor network states

We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states(TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.     

Comments on the properties of one- and two-body double tensor operators

Recently, the parity, charge, time and Hermitian conjugation properties of one-body tensor operators have been reexamined and the Racah algebra has been formally extended to two-body tensor operators. In this paper we consider several important aspects related to these problems. First, we present a proof of the communication relations for two-body operators which was previously postulated. Then, comparing the reduced matrix elements for one- and two-body operators we find the normalization constant for the latter. We subsequently show that the P- and T-conjugation relations for tensor operators are relativistically invariant. Finally, we analyze the question of Hermitian conjugation of double tensor operators and conclude that previously stated conditions on their ranks were too restrictive and resulted in omissions of some terms from theoretical analyses. We show examples of tensor operators which were customarily neglected but indeed should be retained in the effective Hamiltonian.     

The affine geometry of the Lanczos H-tensor formalism

We identify the fiber-bundle-with-connection structure that underlies the Lanczos H-tensor formulation of Riemannian geometrical structure. We consider linear connections to be type (1,2) affine tensor fields, and we sketch the structure of the appropriate fiber bundle that is needed to describe the differential geometry of such affine tensors, namely the affine frame bundleA ₁ ² M with structure groupA ₁ ² (4) =GL(4) T ₁ ^{2 4} over spacetimeM. Generalized affine connections on this bundle are in 1-1 correspondence with pairs(, K) onM, where thegl(4)-component denotes a linear connection and the T ₁ ^{2 4}-componentK is a type (1,3) tensor field onM. We show that the Lanczos H-tensor arises from a gauge fixing condition on this geometrical structure. The resulting translation gauge, theLanczos gauge, is invariant under the transformations found earlier by Lanczos. The other Lanczos variablesQ _mandq are constructed in terms of the translational component of the generalized affine connection in the Lanczos gauge. To complete the geometric reformulation we reconstruct the Lanczos Lagrangian completely in terms of affine invariant quantities. The essential field equations derived from ourA ₁ ² (4)-invariant Lagrangian are the Bianchi and Bach-Lanczos identities for four-dimensional Riemannian geometry.     

The component gauges in supergravity

We present N = 1 supergravity in superspace gauges where the relation to component supergravity is immediate. Among the new results are the inverse vielbein to all orders in φ, some important components of the connection, a Lorentz transformation between our two “component gauges”, the component transformations for a spinor multiplet and some results concerning the axial current for various matter systems coupled to supergravity.     

The connection between general observers and Lanczos potential

We present some algorithms to find the explicit form of the Lanczos potential in an arbitrary geometry.     

Anisotropy of the elastic double force tensor of oxygen interstitials in vanadium

The anisotropyA-B of the double force tensor of O atoms on octahedral interstitial sites in V was determined in a neutron diffraction study. The applied experimental method bases on the fact that elastic stresses change, depending on the value ofA-B the O populations on octahedral sites with different spatial orientations The population changes were determined from the variations in the Bragg intensities. The anisotropy of the dobule-force tensor was found to beA-B=(7.5±1.5)eV.     

Lanczos Spintensor and GHP Formalism

This work shows how the equations which relate the Lanczos potential K _ijr to the conformal tensor C _abpq, can be structured in a simple form when written in terms of the formalism proposed by Geroch-Held-Penrose. As working examples, we present the immediate construction of K _ijk for any spacetime with Petrov type O, N or III. Our findings are in good agreement with already published results, which indicates a relationship between the spin coefficients and the Lanczos spintensor onto the canonical tetrad.     

Background independent duals of the harmonic oscillator

We show that a class of topological field theories are quantum duals of the harmonic oscillator. This is demonstrated by establishing a correspondence between the creation and annihilation operators and nonlocal gauge invariant observables of the topological field theory. The example is used to discuss some issues concerning background independence and the relation of vacuum energy to the problem of time in quantum gravity.     

The bosonic string in non-conformal gauges

The lagrangian and hamiltonian formalism for a free bosonic relativistic string are considered for arbitrary non-orthonormal or non-orthonormal gauges. We show in detail how one can write an arbitrary metric tensor as a reparametrization of a conformally flat one. By means of this decomposition, the lagrangian and hamiltonian formalisms are explicitly solved. From the result of this classical analysis we are then able to conclude that the quantization yields the same physical results as in the standard orthonormal gauge.We also comment on singularities in Liouville theories for strings.     

Super-symmetry and non-Abelian gauges

We show that the conventional Yang-Mills Lagrangian with the Yang-Mills field interacting with Majorana fermions belonging to the adjoint representation of an internal symmetry group like SU(n) is super-gauge invariant.     

Lanczos Potential for the van Stockung Space-Time

The Lanczos Potential is a theoretical useful tool to find the conformal Weyl curvature tensor C _abcd of a given relativistic metric. In this paper we find the Lanczos potential L _abc for the van Stockung vacuum gravitational field. Also, we show how the wave equation can be combined with spinor methods in order to find this important three covariant index tensor.     

Lanczos Potential and Perfect Fluid Spacetimes

Using method of general observers and the spin coefficient formalism of Newman and Penrose, the Lanczos potential has been studied for perfect fluid spacetimes.     

The connection between the energy-momentum tensor and the tensor field in presence of a mass gap

The conditions under which a tensor field can be regarded as an energy-momentum tensor are discussed. The problem connected with dilatational and conformal symmetries are exhibited.