In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincaré group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the (homogeneous) Lorentz group. We investigate the possibility of constructing fields that transform under the full representation of the Poincaré group. We show that such fields can be consistently constructed, although the Lagrangians that describe them exhibit explicit dependence on the space-time coordinates. The inclusion of gravity within the framework of the Poincaré gauge theory is then discussed. A new feature that occurs is that the translational gauge fields enter the covariant derivative of matter fields. The Poincaré-gauge approach works still well and leads to interesting consequences. The detailed discussion of the Dirac field is presented and the relation to the earlier accounts on Poincaré-spinors is drawn. Another example that is considered is the Poincaré-vector field. The presentation has a partly didactic character and is addressed to all the readers who are interested in the rudiments of quantum field theory and the gauge description of gravity.
We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation…
We analyze possible local extensions of the Poincaré symmetry in light-cone gravity in four dimensions. We use a formalism where we represent the algebra on the two physical degrees of freedom, one with helicity $2$ and the other with helicity $-2$. The representation is non-linearly realized and one of the light-cone momenta is the Hamiltonian, which is hence a non-linear generator of the algebra. We find that this can be locally realized and the Poincaré algebra extended to the BMS symmetry without any reference to asymptotic limits.
We demonstrate that Einstein's general relativity theory arises as a special case in the framework of the Poincaré gauge theory of gravity under the assumption of a suitable nonminimal coupling of matter to the Riemann-Cartan geometry of spacetime.
We give an introductory overview of the classical Poincaré gauge theory of gravity formulated on the spacetime manifold that carries the Riemann-Cartan geometry with nontrivial curvature and torsion. After discussing the basic mathematical structures at an elementary level in the framework of the standard tensor analysis, we formulate the general dynamical scheme of Poincaré gauge gravity for the class of Yang-Mills type models, and consider a selected number of physically interesting consequences of this theory.
We analyse the parity violation issue in the Poincaré gauge theory of gravity for the two classes of models which are built as natural extensions of the Einstein-Cartan theory. The conservation laws of the matter currents are revisited and we clarify the derivation of the effective Einstein field equation and the structure of the effective energy-momentum current for arbitrary matter sources.
Null Infinity and Unitary Representation of The Poincare Group
在Pasterski-Shao-Strominger的基础上，我们在无质量粒子的单粒子希尔伯特空间中构造了一个新的态基，作为标准Wigner态的线性组合。在洛伦兹变换下，新的基态变换为酉主连续级数表象。如果我们考虑零动量\textit{direction}而不是零动量的小群，则可以得到这些态。用维格纳态来定义态，使得在此基础上研究时空平移的作用更为容易。通过考虑时空平移的影响，我们证明了\textit{the dynamics of massless particles described by these states takes place completely on the null-infinity of the Minkowski space}。在此基础上，我们对该理论进行了二次修正，得到了一个生活在零无限上的自由无质量粒子的酉显庞加莱不变（场）理论。在这种情况下，零无限的出现纯粹是群理论上的，与体时空没有任何关系。在这幅图中，BMS对无质量粒子的作用是自然的。作为副产品，我们推广了无质量粒子的共形初级波函数，使时空平移的作用变得简单。使用这些波函数，我们写下修改的梅林（傅立叶）变换的S-矩阵元素。结果振幅是庞加莱协变的。在庞加莱变换下，它像插入零无限各个点的非均匀$SL(2,\mathbb{C})$（$ISL(2,\mathbb{C})$）的原色的积一样进行变换。定义了…
The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincaré gauge gravity theory. The class of models with the most general Lagrangians of the Yang-Mills type constructed from all possible quadratic invariants of the curvature and the torsion is considered, including both parity-even and parity-odd sectors. We find the models in which the weak and strong versions of the generalized Birkhoff theorem are valid, by making use of the double duality technique.
We investigate the Poincaré approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)$_k$ WZW models provide unitary examples for which the Poincare series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all …
Poincare invariant gravity with local supersymmetry as a gauge theory for the M-algebra
在这里，我们考虑一个引力作用量具有局部庞加莱不变性，这是由10维欧拉密度的维延给出的。证明了该作用的局部超对称扩张要求该代数是N=1超Poincare代数的极大扩张.由此产生的作用量描述了M-代数的规范理论，而不是Cremmer-Julia-Scherk的11维超引力理论。该理论允许一类形式为S^{10-d} x Y_{d+1}的真空解，其中Y_{d+1}是R与d维时空的翘曲积。结果表明，仅当d=4且宇宙学常数为正时，引力子的非平凡传播子才存在。这个解周围度规的扰动再现了四维德西特时空周围线性化的广义相对论。
Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence …
We perform a manifestly covariant quantization of a Weyl invariant, i.e., a locally scale invariant, scalar-tensor gravity in the extended de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance and a new scalar gauge for Weyl invariance within the framework of BRST formalism. It is shown that choral symmetry, which is a Poincar${\rm{\acute{e}}}$-like $\IOSp(8|8)$ supersymmetry in case of Einstein gravity, is extended to a Poincar${\rm{\acute{e}}}$-like $\IOSp(10|10)$ supersymmetry. We point out that there is a gravitational conformal symmetry in quantum gravi…
