A possible topological interpretation of the Barbero-Immirzi parameter
Simone Mercuri
备注：
10 pages, based on a talk given at the III Stueckelberg workshop on Relativistic Field Theories, July 8-18, 2008, Pescara (Italy). V2: minor corrections in section II, major corrections in section IV
A possible topological interpretation of the Barbero-Immirzi parameter is proposed. Classically, by generalizing the Holst action to torsional spacetimes, we construct a precise analogy between the Barbero--Immirzi parameter and the $θ$-angle of Yang-Mills gauge theories, where the role of the Pontryagin class is played by a well known topological term containing the Holst modification, the Nieh--Yan density. Quantum mechanically, the same analogy requires to study the large gauge sector of the theory. In particular, it is argued that the large sector of the gauge group can be correlated with the Nieh-Yan density, while the Barbero-Immirzi parameter plays the role of the free angular parameter of the large gauge transformations.
We consider General Relativity as a limit case of the Scalar-Tensor theory with Barbero-Immirzi field when the field tends to a constant. We use Shapiro time delay experimental limit of $1/w = (2.1 \pm 2.3)10^{-5}$ provided by the Cassini spacecraft to find the Barbero-Immirzi parameter value.
We introduce a covariant formulation of Barbero-Immirzi connections, which are used in Loop Quantum Gravity to describe gravity. We show that Barbero-Immirzi connections can be uniquely defined out of a given spin connection for any $(n+1)$-dimensional lorentzian manifold which is spin. A remarkable result is that the presence of a real Barbero-Immirzi parameter is a feature unique to the $4$-dimensional case.
Canonical description of Pontryagin and Euler classes with a Barbero-Immirzi parameter
Instituto de Física, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理研究所）；Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla（普埃布拉自治大学物理数学科学学院）
The Barbero-Immirzi parameter ($γ$) is introduced in loop quantum gravity (LQG) whose physical significance is still a biggest open question; because of its profound traits. In some cases, it is real-valued; while, it is complex-valued in other cases. This parameter emerges out in the process of denoting a Lorentz connection with non compact group $SO(3,1)$ in the form of a complex connection with values in a compact group of rotations, either $SO(3)$ or $SU(2)$. Initially, it was appeared in the Ashtekar variables. Fernando Barbero proposed its possibility to include within formalism. Its pre…
The form of Hamiltonian and Diffeomorphism constraints in Sen-Ashtekar-Barbero-Immirzi variables is well known for the spacelike 3+1 ADM foliation. It is also known that Sen-Ashtekar-Barbero-Immirzi connection can be introduced only in 3 dimensional space and does not work for $D > 3$. The reason it works in $D = 3$ is due to existence of isomorphism between $so(3)$ algebra and $R^3$ space with vector product. It turns out that similar isomorphism exists between $so(2,1)$ algebra and $R^3_{2,1}$ space algebra with respect to its vector product. By using this isomorphism we find both analog of …
We carry out the complete variational analysis of the Barbero--Immirzi--Holst Lagrangian, which is the Holst Lagrangian expressed in terms of the triad of fields $(θ, A, κ)$, where $θ$ is the solder form/spin frame, $A$ is the spacetime Barbero--Immirzi connection, and $κ$ is the extrinsic spacetime field. The Holst Lagrangian depends on the choice of a real, non zero Holst parameter $γ\neq 0$ and constitutes the classical field theory which is then quantized in Loop Quantum Gravity. The choice of a real Immirzi parameter $β$ sets up a one-to-one correspondence between pairs $(A, κ)$ and spin …
Action-level characterization of gravitational-wave propagation in dynamical Barbero--Immirzi gravity
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台射电天文与技术重点实验室）；Shanxi Province Intelligent Optoelectronic Sensing Application Technology Innovation Center, Yuncheng University（运城学院山西省智能光电传感应用技术创新中心）；Departamento de Física Teórica, IF-UERJ（里约热内卢州立大学理论物理研究所）；College of Mechanical and Electrical Engineering, Tarim University（塔里机械与电气工程学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿物理研究所）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
Dynamical Barbero--Immirzi field coupled to quintessence: gravitational-wave propagation constraints and next-generation forecasts
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台射电天文与技术重点实验室）；Shanxi Province Intelligent Optoelectronic Sensing Application Technology Innovation Center, Yuncheng University（运城学院山西省智能光电传感应用技术创新中心）；Departamento de Física Teórica, IF-UERJ（里约热内卢州立大学理论物理系）；College of Mechanical and Electrical Engineering, Tarim University（塔里米大学机电工程学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿物理研究所）
We revisit the predictions for the duration of the inflationary phase after the bounce in loop quantum cosmology. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, the Starobinsky and the Higgs-like symmetry breaking potential with different values for the vacuum expectation value. Our setup can easily be extended to other forms of primordial potentials than the ones we have considered. Independently on the details of the contracting phase, if the dynamics starts sufficiently in the far past, the kinetic ene…
