Search results for "Tensor field"
showing 10 items of 23 documents
A new functional flow equation for Einstein-Cartan quantum gravity
2015
We construct a special-purpose functional flow equation which facilitates non-perturbative renormalization group (RG) studies on theory spaces involving a large number of independent field components that are prohibitively complicated using standard methods. Its main motivation are quantum gravity theories in which the gravitational degrees of freedom are carried by a complex system of tensor fields, a prime example being Einstein-Cartan theory, possibly coupled to matter. We describe a sequence of approximation steps leading from the functional RG equation of the Effective Average Action to the new flow equation which, as a consequence, is no longer fully exact on the untruncated theory sp…
Decay of axial-vector mesons into VP andPγ
2004
We propose a phenomenological Lagrangian for the decay of the SU(3) nonets of the axial-vector mesons of J{sup PC}=1{sup +-},1{sup ++} into a vector meson and a pseudoscalar constructed with tensor fields for the vector and axial-vector mesons. The formulation leads to a good reproduction of the different decay branching ratios and assuming vector meson dominance (VMD) it also leads to good results for the radiative decay of the a{sub 1} into pion and photon, and in agreement with the structure proposed in the chiral tensor formulation of radiative decay of axial-vector mesons. The two SU(3) parameters and the mixing angle of K{sub 1A} and K{sub 1B} needed to give the physical K{sub 1}(1270…
Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
1996
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well …
New Limit on Lorentz-Invariance- andCPT-Violating Neutron Spin Interactions Using a Free-Spin-PrecessionHe3-Xe129Comagnetometer
2014
We report on the search for a $CPT$- and Lorentz-invariance-violating coupling of the $^{3}\mathrm{He}$ and $^{129}\mathrm{Xe}$ nuclear spins (each largely determined by a valence neutron) to posited background tensor fields that permeate the Universe. Our experimental approach is to measure the free precession of nuclear spin polarized $^{3}\mathrm{He}$ and $^{129}\mathrm{Xe}$ atoms in a homogeneous magnetic guiding field of about 400 nT using ${\mathrm{LT}}_{C}$ SQUIDs as low-noise magnetic flux detectors. As the laboratory reference frame rotates with respect to distant stars, we look for a sidereal modulation of the Larmor frequencies of the colocated spin samples. As a result we obtain…
The structure of Fedosov supermanifolds
2009
Abstract Given a supermanifold ( M , A ) which carries a supersymplectic form ω , we study the Fedosov structures that can be defined on it, through a set of tensor fields associated to any symplectic connection ∇ . We give explicit recursive expressions for the resulting curvature and study the particular case of a base manifold M with constant holomorphic sectional curvature.
Quasi-Continuous Vector Fields on RCD Spaces
2021
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined $\mathfrak {m}$ -a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector fields have a 2-capacity-a.e. uniquely defined quasi-continuous representative.
One loop integrals revisited
1992
We present a new calculation of the well-known one-loop two-point scalar and tensor functions. We also present a systematic reduction to a certain class of functions which minimizes the effort for calculating tensor integrals drastically. We avoid standard techniques such as Feynman parametrization and Wick rotation.
Two-loop tensor integrals in quantum field theory
2004
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of smoothness algorithms already employed for the numerical evaluation of ordinary scalar functions, are introduced for each family of diagrams.
Tensor Operators and the Wigner-Eckart Theorem
2007
In this chapter we pave the way to the use of the coupling methods of Chap. 1 for manipulating operators and their matrix elements. To enable smooth application of the angular momentum methods, we introduce so-called spherical tensor operators. Spherical tensors can be related to Cartesian tensors. A Cartesian tensor of a given Cartesian rank can be reduced to spherical tensors of several spherical ranks. There is a very convenient procedure, the so-called Wigner-Eckart theorem, to separate the part containing the projection quantum numbers from the rest of the matrix element of a spherical tensor operator. The remaining piece, called the reduced matrix element, is rotationally invariant an…
Intrinsic characterization of space‐time symmetric tensors
1992
This paper essentially deals with the classification of a symmetric tensor on a four‐dimensional Lorentzian space. A method is given to find the algebraic type of such a tensor. A system of concomitants of the tensor is constructed, which allows one to know the causal character of the eigenspace corresponding to a given eigenvalue, and to obtain covariantly their eigenvectors. Some algebraic as well as differential applications are considered.