External Tensor Field Research Articles

Renormalization of vector fields with mass-like coupling in curved spacetime

Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum abelian vector field with a non-derivative coupling to an external tensor field in curved spacetime in four dimensions is considered. Relatively explicit expressions are obtained which are manifestly local but non polynomial in the external fields. Our result is shown to reproduce existing ones in all particular cases considered. Internal consistency with Weyl invariance is also verified.

Relativistic point particles in external fields

Motion of a point particle (a particle without any internal structure) in the context of special relativity is investigated. The study is based on the action principle with either time or the proper time regarded as the evolution parameter. Actions corresponding to the motion of particle in general external tensor fields are obtained.

From spinning conformal blocks to matrix Calogero-Sutherland models

In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of [1] is extended to arbitrary dimensions and to the case of boundary two-point functions. In particular, we construct the potential for any set of external tensor fields. Some of the resulting Schrödinger equations are mapped explicitly to the known Casimir equations for 4-dimensional seed conformal blocks. Our approach furnishes solutions of Casimir equations for external fields of arbitrary spin and dimension in terms of functions on the conformal group. This allows us to reinterpret standard operations on conformal blocks in terms of group-theoretic objects. In particular, we shall discuss the relation between the construction of spinning blocks in any dimension through differential operators acting on seed blocks and the action of left/right invariant vector fields on the conformal group.

One-loop divergences in massive gravity theory

The one-loop divergences are calculated for the recently proposed ghost-free massive gravity model, where the action depends on both metric and external tensor field f. The non-polynomial structure of the massive term is reduced to a more standard form by means of auxiliary tensor field, which is settled on-shell after quantum calculations are performed. As one should expect, the counter-terms do not reproduce the form of the classical action. Moreover, the result has the form of the power series in f.

Modified approach for calculating tensor vacuum susceptibility

Abstract By differentiating the dressed quark propagator with respect to a constant external tensor field, the linear response of the nonperturbative dressed quark propagator in the presence of the constant external tensor field can be obtained. From this we extract a general expression for the vacuum susceptibility which is needed in the QCD sum rule external field method for the coupling of tensor current to hadrons and compare it with the previous approaches. The numerical value of the tensor vacuum susceptibility are calculated within the framework of the rainbow-ladder approximation of the Dyson–Schwinger approach.

QCD sum rule calculation for the tensor charge of the nucleon.

The nucleon's tensor charges (isovector ${g}_{T}^{v}=\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d$ and isoscalar ${g}_{T}^{s}=\ensuremath{\delta}u+\ensuremath{\delta}d$) are calculated using the QCD sum rules in the presence of an external tensor field. In addition to the standard quark and gluon condensates, new condensates described by vacuum susceptibilities are induced by the external field. The latter contributions to ${g}_{T}^{v}$ and ${g}_{T}^{s}$ are estimated to be small. After deriving some simplifying formulas, a detailed sum rule analysis yields ${g}_{T}^{v}=1.29\ifmmode\pm\else\textpm\fi{}0.51$ and ${g}_{T}^{s}=1.37\ifmmode\pm\else\textpm\fi{}0.55$, or $\ensuremath{\delta}u=1.33\ifmmode\pm\else\textpm\fi{}0.53$ and $\ensuremath{\delta}d=0.04\ifmmode\pm\else\textpm\fi{}0.02$ at the scale of 1 Ge${\mathrm{V}}^{2}$.

Tensor Charge of the Nucleon from QCD Sum Rules

The nucleon's tensor charges (isovector gTv = δu - δd and isoscalar gTs = δu + δd) are calculated using the QCD (quantum chromodynamics) sum rules in the presence of an external tensor field. By combining the mass sum rule of nucleon, we derive a simplified form for proton tensor charges, which gives gTv = 1.27 and gTs = 1.31, or δu = 1.29 and δd = 0.02 at the scale of nucleon mass, with an uncertainty about 20%.

Axial anomalies in external tensor fields

The calculation of the anomaly of the axial current of Dirac fermions in external antisymmetric tensor fields of odd rank is considered. A sequence of one-dimensional supersymmetric models is presented and it is shown that their supercharges are, after quantization, Dirac operators in the external tensor fields, while their Witten partition function is the anomaly of the axial current. It is shown that the action in the corresponding functional integral for the partition function is different from the classical action. The semiclassical approximation gives the anomaly only in the case of an external tensor field of third rank with zero exterior derivative, and it is calculated in this case for arbitrary dimension. The interpretation of this field as an external gravitational field with torsion and the connection with the results of Witten and Alvarez-Gaume and the Atiyah-Singer theorem are discussed.