论文标题
在最小巨大的3D重力和外部代数形式上的旋转体相互作用中的物质耦合
Matter coupling in Minimal Massive 3D Gravity and spinor-matter interactions in exterior algebra formalism
论文作者
论文摘要
在这项工作中，通过采用外部代数形式主义，我们首先考虑到Lagrangian是与连接无关的，然后考虑物质耦合是连接依赖性的，我们首先考虑了最小的大量3D重力（MMG）。 MMG中的物质耦合以前已在Arvanitakis {\ it等}的工作中进行了研究（2014 {\ itclass。tastumgrav。} {\ bf 31} 235012）在Tensorial note中，该物质lagrangian认为lagrangian被认为是连接独立的。在本文的第一部分中，我们通过使用不同形式的语言来重新审视与连接无关的物质耦合。我们得出MMG场方程并构建相关源2形式。我们还获得了这种形式主义中的一致关系。接下来，我们检查了Lagrangian与连接有关的情况。特别是，我们专注于旋转旋转耦合，并通过明确构建源项来获得MMG场方程。我们还获得了一致性关系，即源项应满足，以使旋转耦合的MMG方程保持一致。
In this work, by employing the exterior algebra formalism, we study the matter coupling in Minimal Massive 3D Gravity (MMG) by first considering that the matter Lagrangian is connection-independent and then considering that the matter coupling is connection-dependent. The matter coupling in MMG has been previously investigated in the work Arvanitakis {\it et al} (2014 {\it Class. Quantum Grav.} {\bf 31} 235012) in tensorial notation where the matter Lagrangian is considered to be connection-independent. In the first part of the present paper, we revisit the connection-independent matter coupling by using the language of differential forms. We derive the MMG field equation and construct the related source 2-form. We also obtain the consistency relation within this formalism. Next, we examine the case where the matter Lagrangian is connection-dependent. In particular, we concentrate on the spinor-matter coupling and obtain the MMG field equation by explicitly constructing the source term. We also get the consistency relation that the source term should satisfy in order that spinor-matter coupled MMG equation be consistent.
