Janusz Garecki
Here we present a new method to study stability of the solutions to the Einstein equations. This method uses the canonical superenergy tensors which have been introduced in past in our papers.
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Here we present our actual point of view on the canonical superenergy tensors.
Many years ago we have introduced into general relativity, {\bf GR}, the canonical superenergy tensors, $S_i^{~k}$, and the canonical angular supermomentum tensors, $S^{ikl}=(-)S^{kil}$, matter and gravitation. We have obtained these tensors by special averaging of the differences of the canonical energy-momentum and canonical angular momentum. The averaging was performed in Riemann normal coordinates, {\bf RNC(P)}; {\bf P} is beginning of these coordinates. About four years ago we have observed that these tensors can also be obtained in other, simpler way, by using the canonical superenergy a…
Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups
在以前的论文中，我们表明，电磁超能张量，Chevreton张量，产生一个保守的电流时，有一个超曲面正交Killing矢量。此外，电流与Killing矢量成比例。本文的目的是推广这一结果的情况下，我们有一个两参数的阿贝尔等距群，正交传递的非零表面。结果表明，对于无源电磁场的四维Einstein-Maxwell理论，相应的超能流位于群的轨道上，并且是守恒的。类似的结果也适用于Chevreton张量和Bach张量的迹，也适用于标量场的超能的Einstein-Klein-Gordon理论。这与Bel张量具有这些性质的事实以及在引力场和物质场之间构造守恒混合流的可能性有很好的联系。
In this work we present a geometric identity involving the Bel-Robinson tensor which is formally similar to the Sparling identity (which involves the Einstein tensor through the Einstein 3-form). In our identity the Bel-Robinson tensor enters through the {\em Bel-Robinson 3-form} which, we believe, is introduced in the literature for the first time. The meaning of this identity is that it is possible to formulate a {\em generic} conservation law for the quantity represented by the Bel-Robinson tensor (superenergy). We also show how one can use the Bel-Robinson 3-form to estimate the components…
Conserved superenergy currents
我们再次利用能量动量张量和所谓的“超能”张量之间的类比，以便在Killing矢量存在的情况下建立守恒电流。首先，我们在非常一般的情况下导出了引力超能流的无发散性质，即使超能张量本身不是无发散的。相关的守恒量明确计算Reissner-Nordstrom和Schwarzschild解决方案。其余的情况，当上述电流不守恒时，导致在引力场和其他物理场之间交换某些超能量的可能性，使得总的混合电流可以守恒。实际上，这种可能性最近已被证明适用于Einstein-Klein-Gordon场方程系统。通过使用一个足够的家庭已知的精确解，我们提出了明确的和完全不明显的例子，这样的混合守恒电流。
Superenergy tensors for a massive scalar field
定义了在闵可夫斯基时空中传播的实质量标量场的偶数秩2（n+1）超能张量的一般类。在n=1的情况下，我们建立了这个类是一个两参数的家庭，减少到一个唯一的张量W（直到一个常数因子）时，需要的四个指标的完全对称。我们证明了超能密度$W^{\al\ba\ga\da}u_{\al}u_{\ba}u_{\ga}u_{\da}$相对于任何类时单位矢量$u$是正定的，超动量密度$W^{\al\ba\ga\da}u_{\ba}u_{\ga}u_{\da}$是类时或零矢量（$W^{\al\ba\ga\da}$代表W）.接下来，我们找到一个无限多的秩为2+p+q的保守张量$U_{(p,q)}$，当p=q=n时，我们称之为n阶弱超能张量。我们证明了$U_{(1,1)}$和W产生相同的总超能和相同的总超动量。然后，利用正则量子化方案，我们明确地构造了对应于W和每个弱超能张量$U_{(n,n)}$的超哈密顿量和超动量算符。最后，我们展示了电磁场和引力场的超能张量的两参数族。
Superenergy and Supermomentum of Goedel Universes
我们回顾了广义相对论中的正则超能张量和正则角超动量张量，并计算了时空均匀哥德尔宇宙中的正则超能张量和正则角超动量张量，以表明这两个张量一般不会消失。我们考虑了1949年原始的充满灰尘的无压因果哥德尔模型和Rebou \c cas和Tiomno的充满标量场的因果哥德尔模型。在因果模型中，物质超能的非零分量不同于引力的非零分量。物质和引力的角超动量张量也不为零，这只是反映了哥德尔宇宙旋转的事实。然而，超动量张量的轴向（完全反对称）和矢量部分消失了。有趣的是，超能量对因果关系是{PDMATHAMN敏感}的，在因果模型中引力的超能密度$_g S_{00}$是{PDMATHAMN正}，而在因果模型中超能密度$_g S_{00}$是{ \it负}。这意味着超能量可以作为宇宙学中因果关系的判据，并证明是有用的。
On the structure of the new electromagnetic conservation laws
新的电磁守恒定律最近被提出：在没有电磁流的情况下，Chevreton超能张量的迹，$H_{ab}$在四维（a）爱因斯坦时空的测试场，（b）爱因斯坦-麦克斯韦时空中是无发散的。随后，人们指出，与平坦空间类似，对于爱因斯坦时空，Chevreton超能量张量$H_{ab}$的迹线可以以作用于测试场的能量动量张量$T_{ab}$的广义波算符$\square_L$的形式重新排列，即，$H_{ab}=\square_LT_{ab}/2$。在这封信中，我们表明，对于完全非线性理论中的Einstein-Maxwell时空，虽然Chevreton超能张量$H_{ab}$的迹线可以再次以作用于电磁能动量张量的广义波算符$\square_G$的形式重新排列，但在这种情况下，结果也关键地依赖于Einstein方程;因此，我们认为张量$H_{ab}=\square_GT_{ab}/2$的无发散性除了$T_{ab}$的无发散性之外，还有重要的独立内容.
The averaged tensors of the relative energy-momentum and angular momentum in general relativity
在给出张量的法向坐标{ \bf NC（P）}中，至少存在几种不同的能量-动量和角动量差的平均。所获得的平均量在数学上是等效的，因为它们仅在常数标量尺寸因子上不同。我们的论文[1-8]采用了其中一种平均方法，给出了{ \it正则超能和角超动量张量}。在本文中，我们提出了另一个平均的能量动量和角动量的差异，它给出了张量的能量动量和角动量密度与适当的尺寸。但是这些平均的能量-动量和角动量张量，与正则超能和角超动量张量密切相关，{ \it依赖于某个基本长度L}。本文得到的引力场的平均能量动量张量和角动量张量，可以象正则超能张量和角超动量张量一样，用于协调该场的独立局部（也可以是整体）分析。
Energy, angular momentum, superenergy and angular supermomentum in conformal frames
我们找到了爱因斯坦能量动量复合体、Bergmann-Thomson角动量复合体、引力和物质的超能量张量和角超动量张量等能量量的保角变换规则。我们表明，爱因斯坦复形和Bergmann-Thomson复形的物质部分的共形变换规则是相当简单的，而它们的引力部分的变换规则更复杂。我们还发现，除了纯引力的情况外，物质的超能张量和引力的超能张量的变换规则是相当复杂的。在这种特殊情况下，超能密度以及超能密度与物质能量密度之和是保角变换的不变量。此外，在这种情况下，共形不变量也是Bel-Robinson张量，它是超能张量的一部分。至于引力的角超动量张量--它的变换规则即使对于纯引力也是相当复杂的，但对于物质的角超动量张量却不是这样。在研究了保角变换的一些技巧之后，我们还发现了曲率不变量的保角变换规则，特别是任意维时空中的Gauss-Bonnet不变量。
Here we propose a new method to study gravitational stability of the solutions to the Einstein equations. This method uses the canonical superenergy density and it is different from approaches already used (Lyapunov's stability, dynamical systems). Our method is very alike to the procedure of finding the stable minima of the interior energy U for a dynamical system.
Applications of Super-Energy Tensors
在这篇文章中，我打算给出一个总结的新的相关结果，通过使用一般的超能张量。在快速回顾了这些张量的定义和性质之后，介绍了它们的几个数学和物理应用。特别是，它们的兴趣和有用性被提到或明确分析在1）一般场的因果传播的研究; 2）在Ricci平坦时空中存在无穷多个守恒量; 3）不同的引力理论，如爱因斯坦的广义相对论或，比如说，$n=11$超引力; 4）一些标量的出现可能与熵或品质因数有关; 5）不同物理场之间超能交换的可能性和混合守恒流的出现。
From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
从爱因斯坦-嘉当正则理论出发，将引力-旋量耦合系统的态泛函按Nieh-Yan泛函的指数重新标度，导出了含费米子的广义相对论的Ashtekar-Barbero约束.一个参数量化模糊性自然出现，并且可以与Immirzi参数相关联。
Different canonical formulations of Einstein's theory of gravity
我们描述了爱因斯坦引力理论中经典正则形式主义的四个最著名的版本：Arnovitt-Deser-Misner形式主义，Faddeev-Popov形式主义，通常形式的四分形式主义，以及最适合于构建引力环理论的形式的四分形式主义，这是现在正在发展的。我们提出了这些形式主义的规范转换。本文主要是为了教学目的而写的。
Canonical Quantization of Spherically Symmetric Einstein-Scalar Field Solutions
本文利用 Dirac 约束量子化方法研究含无质量标量场的球对称时空，得到 Wheeler-DeWitt 方程，给出动量约束的一般解，并在静态情形获得完整解。
Static axisymmetric Einstein spaces with a cosmological constant and the limitation of canonical Weyl coordinates
本文证明在具有非零宇宙学常数的爱因斯坦空间中，规范Weyl坐标$W=\rho$仅在$\Lambda=0$时局部可行，并推导了约化的爱因斯坦-Λ场方程，以Kottler度规为例说明面积函数不再调和。
First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
我们规定了18个变量的选择，在所有的铸造方程的广义相对论的完全非线性特征制定的一阶准线性规范形式。在分析的层次上，这种类型的公式使我们能够对解的存在性做出具体的陈述。此外，它提供了具体的优点，数值应用，因为它现在成为可能，将先进的数值技术的一阶系统，迄今为止还不适用于特征问题的爱因斯坦方程，以及在提供一个框架，统一处理的真空和物质问题。这与精确模拟恒星核坍缩等天体物理场景中发射的引力波有关。
A Reexamination of the Canonical Structure of the Einstein-Hilbert Action in First-Order Form
本文考虑了Einstein-Hilbert作用量S_d（d>2）的一阶正则分析。我们采用保守的方法来使用狄拉克约束形式主义，我们不使用运动方程，这是独立的时间导数和对应的第一类约束，以消除领域。应用狄拉克程序，我们发现，初级约束导致二级约束，这是不涉及时间导数的运动方程，这些二级约束是第一类意味着新的三级约束，也是第一类。一旦用这些约束条件和相应的规范条件消除了S_d中的非动力学自由度，相空间中就剩下d（d-3）个自由度。我们还考虑了在一阶形式中非相互作用引力子的简单极限情况以及在Einstein-Hilbert作用量中加入无质量标量场的作用量的影响。
Quantization of a 2D Minisuperspace Model in Dilaton-Einstein Gravity
本文研究了一个描述静态球对称位形或Kantowski - Sachs类宇宙的爱因斯坦引力加介子的小超空间模型。我们开发的正则形式主义和确定产生刚性对称的哈密顿量的正则量。量子化是由狄拉克和减少的方法。这两种方法都导致了相同的正定希尔伯特空间。
A Directive for obtaining Algebraically General Solutions of Einstein Equations Based on the Canonical Killing Tensor Forms
本文利用标准 Killing 张量形式与反对称零标架内的 Lorentz 变换，构造含宇宙学常数的真空柱对称代数通解，并提出推广求解方针。
This paper is devoted to the analysis of the covariant canonical formalism of $F(R)$ gravity in Einstein frame. We also find canonical transformation between covariant canonical formulation of F(R) gravity in Jordan frame and Einstein frames and we also determine corresponding generating function.
The reduced phase space of spherically symmetric Einstein-Maxwell theory including a cosmological constant
本文将球对称（量子）引力的正则处理推广到最简单的物质耦合，即有或没有宇宙学常数的球对称麦克斯韦理论。量子化的基础上，这是协调的质量和电荷，以及他们的正则共轭动量，其几何解释进行了探讨的约化相空间。约化相空间的维数取决于所选择的拓扑，与纯（2+1）引力的情况非常相似。我们研究了几个概念和技术细节，可能是感兴趣的全（3+1）重力。我们使用Ashtekar引入的新的规范变量，这极大地简化了分析。
Causal Propagation of Constraints and the Canonical Form of General Relativity
对爱因斯坦演化方程的新双曲系统的研究表明，"切片密度“$α(t,x)$可以自由指定，而延时$N = αg^{1/2}$不能。在Arnowitt-Deser-Misner作用量原理中实现这个小的变化会导致与爱因斯坦方程一致的正则方程，无论约束是否满足。约束函数，独立于它们的值，然后根据一阶对称双曲系统，其特征锥是光锥传播。这一结果来自于二次压缩的Bianchi恒等式，并构成了规范形式主义中约束“代数”的核心内容。
Conical Singular Solutions in (2+1)-Dimensional Gravity Employing the ADM Canonical Formalism
在ADM正则形式下研究了（2+1）维爱因斯坦引力理论的拓扑解。在爱因斯坦理论中，当宇宙常数为宇宙学常数时，在封闭的de Sitter宇宙解中，出现了一个作为拓扑缺陷的圆锥奇点。利用de Broglie-Bohm解释研究了圆锥奇点的量子效应。在封闭的de Sitter宇宙中得到了有限的量子隧穿效应，而在开放的宇宙中没有得到量子效应。
Reduced Phase Space Quantization of spherically symmetric Einstein-Maxwell-Theory including a cosmological constant
本文给出了球对称（量子）引力与球对称麦克斯韦理论耦合的正则化处理方法，无论有无宇宙学常数。量子化的基础上，这是协调的质量和电荷，以及他们的正则共轭动量，其几何解释进行了探讨的约化相空间。约化相空间的维数取决于所选择的拓扑，与纯（2+1）引力的情况非常相似。我们还比较了减少相空间量化的代数量化。总的来说，我们观察到，目前的模型作为一个有趣的试验场完全（3+1）重力。我们使用新的规范变量引入Ashtekar这大大简化了分析。
Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Ein…
The definition of physical states is the main technical issue of canonical approaches towards Quantum Gravity. In this work, we outline how those states can be found in Einstein-Cartan theory via a continuum limit and they are given by finite dimensional representations of the Lorentz group.
Canonical quantization of modified non-gauge invariant Einstein-Maxwell gravity and stability of spherically symmetric electrostatic stars
本文通过正则量子化方法研究非最小耦合且无U(1)对称性的爱因斯坦-麦克斯韦引力下静电星的稳定性，发现其稳定性不受规范场影响，且量子化时空无事件视界和表观视界，荷质比为常数。
Quasi-Local Energy Conservation Law Derived From The Einstein's Equations
从广义相对论的正则（2，2）形式中类时边界面上的真空爱因斯坦方程出发，导出了准局域能量守恒定律。在渐近平坦极限和球对称时空中，准局域能量和能流积分与标准结果一致。
Quantum Einsteinian Cubic Cosmology
本文研究了爱因斯坦立方引力在最小超空间量子宇宙学中的应用，通过正则量子化方法求解了非标准的 Wheeler-DeWitt 方程，并得到不同空间几何情况下的精确解和 WKB 解。
A Canonical Analysis of the First Order Einstein-Hilbert Action
当以一阶形式表示时，Dirac约束形式被应用于d（d>2）维Einstein-Hilbert作用量，使用度量密度和仿射联络作为独立的场。不涉及时间导数的场方程不用于消除场。初级、次级和三级约束出现，在相空间中留下d（d-3）个自由度。给出了这些约束的Poisson代数。
It has been shown that the canonical structure of the first order Einstein-Hilbert (1EH) action involves three generations of constraints and that these can be used to find the generator of a gauge transformation which leaves the action invariant; this transformation is a diffeomorphism with field-dependent gauge function while on shell. In this paper we examine the relationship between the canonical structure of this action and that of the first order spin-2 (1S2) action, which is the weak field limit of the Einstein-Hilbert action. We find that the weak field limit of the Possion Brackets (P…
Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
我们研究的方法，其中描述重力的独立变量的时空嵌入到一个平坦的高维空间的功能。我们制定了一个规范的形式主义这样一个理论的形式，这需要施加额外的约束，这是爱因斯坦方程的一部分。结果，我们得到了一个具有八参数规范对称性的理论。这个理论在部分规范固定之后，或者在以在附加规范变换下不变的形式重写度规之后，变得等价于爱因斯坦的广义相对论。我们为这样一个理论写行动。
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The Lagrange multiplier 2-forms we use turn out to be precisely the Belinfante-Rosenfeld 2-forms that are needed to symmetrize the canonical energy-momentum tensor of the Majorana spinor.
The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
介绍了爱因斯坦广义相对论的正则形式。这就成为研究量子引力的一种方法的起点，称为量子几何动力学。简要介绍了该方法的主要特点和应用。
We discuss the relation between the canonical Hamilton-Jacobi theory and the De Donder-Weyl Hamilton-Jacobi theory known in the calculus of variations using the examples of a scalar field in curved space-time and general relativity. By restricting ourselves to the Gaussian coordinates we show how the canonical Hamilton-Jacobi equation of general relativity can be derived from the De Donder-Weyl Hamilton-Jacobi formulation of the Einstein equations.
It is shown that Einstein gravitational equations and canonical equations following from the Dirac-Schwinger Hamiltonian in the Faddeev variables coincide. For proving of this at first, the Einstein equations has been rewritten in canonical variables, and after this, the time derivative of the generalized momenta of the gravitational field in Faddeev form has been calculated using canonical Poisson brackets. The results coincide.
On the Canonical Structure of First Order Einstein-Hilbert Action Coupled to Bosonic Matter
一阶形式的d维爱因斯坦-希尔伯特作用量的狄拉克哈密顿公式表明，除了第二第一类约束外，还出现了第三第一类约束，第一类约束中有一个不寻常的非局部泊松括号（PB）代数[8 ]。这种方法是从ADM的不同之处在于，运动方程是独立的时间导数的字段，只有那些对应于第二类约束（在狄拉克约束形式主义的意义上）被用来消除字段的行动。本文考虑了在这种形式下宇宙学项、有质量标量场、Maxwell规范场和Yang-Mills场与一阶EH作用量的耦合，并指出尽管在一阶EH作用量的哈密顿形式及其约束结构上与ADM结果有明显的差别，在玻色子物质存在下的一阶EH作用量的ADM哈密顿公式的一般性质可从该新颖的哈密顿公式导出。在EH作用量上增加一个质量标量场，约束的PB代数保持不变，当杨-米尔斯场或麦克斯韦规范场耦合到EH作用量上时，与EH作用量有关的约束的PB代数接收来自物质场作用量的规范变换的生成元的线性贡献，这些生成元之间形成一个封闭的代数。此外，我们还发现，对于封闭空间，在由第一类约束（包括由物质场产生的约束）定义的约束面上，耦合到玻色物质的EH作用量的哈密顿量弱为零.
Einstein theory can be embedded in Kaluza-Klein theory, and in particular all 4D vacuum solutions can be embedded in 5D (pure) canonical space where spacetime is independent of the extra coordinate. The uniqueness of 5D canonical space is quickly reproven, and its history and implications briefly reviewed. For 4D anti-deSitter space, the 5D space involves a wave running around spacetime, with an associated particle that has a local value of the cosmological 'constant' proportional to the square of the mass.
A note on the Hamiltonian constraint in canonical GR
本文证明了具有宇宙学常数的耦合Einstein-Yang-Mills-Higgs系统的哈密顿约束是相空间和三维空间体积上无量纲泛函的纯Poisson括号.它的潜在后果之一，一类正则量子引力理论的体积算符的本征态的限制，也指出。
Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as a part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over the spatial section. The second class constraints are analyzed and Dirac bracket is defined. Reduction of the phase space is performed and canonical coordinates are introduced.
We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from applying the Faddeev-Popov (FP) procedure directly. Due to the presence of tertiary first class constraints, the measure of the path integral is found to have a substantially different structure from what arises in the FP approach. In addition, the presence of second class constraints leads to non-trivial ghosts, which cannot be absorbed into the normalization of t…
Jordan and Einstein frame are studied under the light of Hamiltonian formalism. Dirac's constraint theory for Hamiltonian systems is applied to Brans-Dicke theory in the Jordan Frame. In both Jordan and Einstein frame, Brans-Dicke theory has four secondary first class constraints and their constraint algebra is closed. We show, contrary to what is generally believed, the Weyl (conformal) transformation, between the two frames, is not a canonical transformation, in the sense of Hamiltonian formalism. This addresses quantum mechanical inequivalence as well. A canonical transformation is shown.
The Dirac constraint formalism is used to analyze the first order form of the Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d - 3) degrees of freedom in phase space. The gauge invariance of the action is discusse…
Spherically Symmetric Geometrodynamics in Jordan and Einstein frames
本文在乔丹框架和爱因斯坦框架中研究球对称几何动力学，通过哈密顿正则变换建立两框架联系，并分析了该变换奇点对两类静态解的影响。
Differential topology and micro-structure of black hole in Einstein-Euler-Heisenberg spacetimes with exponential entropy
本文利用拓扑流映射理论，在指数熵框架下研究爱因斯坦-欧拉-海森堡黑洞的拓扑类与微观结构，通过不同系综分析拓扑荷，并验证稳定性及热力学曲率。
On the canonical equivalence between Jordan and Einstein frames
本文证明在通过规范固定lapse和shift函数得到的约化相空间上，从Jordan框架到Einstein框架的变换是哈密顿正则的，并采用Bergman-Dirac程序以狄拉克括号替代泊松括号，从而将两框架的运动方程解相互映射。
After the study of non-inertial frames in special relativity with emphasis on the problem of clock synchronization (i.e. of how to define 3-space), an overview is given of Einstein canonical gravity in the York canonical basis and of its Hamiltonian Post-Minkowskian (PM) linearization in 3-orthogonal gauges. It is shown that the York time (the trace of the extrinsic curvature of 3-spaces) is the inertial gauge variable describing the general relativistic remnant of the clock synchronization gauge freedom. The dark matter implied by the rotation curves of galaxies can be explained with a choice…
In this work, in the context of modified gravity, a curved spacetime analogous to the "canonical acoustic black hole" is constructed. The source is a self-interacting scalar field which is non-minimally coupled to gravity through the Gauss-Bonnet invariant. The scalar-Gauss-Bonnet coupling function is characterized by three positive parameters: $σ$ with units of $(length)$, $μ$ with units of $(length)^{4}$, and a dimensionless parameter $s$, thus defining a three-parameter model for which the line element of canonical acoustic black hole is a solution. The spacetime is equipped with spherical …
Classical equivalence between Jordan's and Einstein's frame counterparts of F(R) theory of gravity has recently been questioned, since the two produce different Noether symmetries, which couldn't be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time-time component of Einstein's equation, through a Lagrange multiplier to the existence condition for Noether symmetry to show that all the three different canonical structures of F(R) theory of gravity, including the one which follows from Lagrange multiplier techn…
A canonical analysis of RG improved action of the Einstein-Hilbert functional is performed. The gravitational and cosmological constants as function of the space-time coordinates are treated as external non-geometrical fields. Dirac's constraint analysis is performed, in the general case, up to secondary constraints. The constraints are second class and, in general, the problem appears to be technically complicated. This fact suggests studying the Dirac's constraint analysis of the related Brans-Dicke theory. It exhibits a Dirac's constraint algebra similar to Einstein's geometrodynamics excep…
Anomaly in canonical semiclassical gravity
该研究指出半经典爱因斯坦方程的正则形式因约束代数不闭合而不一致，其物质项被替换为量子态中对应算符的期望值。
On the Natural Equivalence Between Canonical and Hilbert Energy Momentum Tensors via Noether's Theorem
本文通过诺特定理，统一导出了规范理论中的规范能量动量张量，并证明了其与爱因斯坦-希尔伯特能量动量张量的自然等价性，同时给出了爱因斯坦场方程的替代推导。
Arising out of a Non-local non-relativistic BEC, we present an Analogue gravity model upto $\mathcal{O}(ξ^{2})$ accuracy in the presence of the quantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime where the series solution of the free minimally coupled KG equation for the large length scale massive scalar modes is derived. We systematically address the issues of the presence of the quantum potential term being the root cause of a UV-IR coupling between short wavelength `primary' modes which are supposedly Hawking radiated through the sonic horizon and the large wavelength …
We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field. For this purpose we use a unimodular decomposition of the three-metric and introduce unimodular-conformal canonical variables. The important feature of this choice is that only the scale part of the three-metric and the rescaled trace part of the extrinsic curvature change under a conformal transformation. This significantly simplifies the constraint analysis and manifestly reveals the conformal properties of a theor…
Canonical quantization of all minisuperspaces with consistent symmetry reductions
本文研究了所有正确复现约简爱因斯坦场方程的爱因斯坦-希尔伯特拉格朗日量的量子化，通过规范对称性约简得到多种时空对称性结构的量子化方法。
We study the coupling of N charged scalar particles plus the electro-magnetic field to ADM tetrad gravity and its canonical formulation in asymptotically Minkowskian space-times without super-translations. We make the canonical transformation to the York canonical basis, where there is a separation between the {\it inertial} (gauge) variables and the {\it tidal} ones inside the gravitational field and a special role of the Eulerian observers associated to the 3+1 splitting of space-time. The Dirac Hamiltonian is weakly equal to the weak ADM energy. The Hamilton equations in Schwinger time gaug…
Lapse function appears as Lagrange multiplier in Einstein-Hilbert action and its variation leads to the (0 0) equation of Einstein, which corresponds to the Hamiltonian constraint equation. In higher order theory of gravity the situation is not that simple. Here, we take up the curvature squared (R^2) action being supplemented by an appropriate boundary term in the background of Robertson-Walker minisuperspace metric, and show how to identify the constraint equation and formulate the Hamiltonian without detailed constraint analysis. The action is finally expressed in the canonical form $A = \i…
Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex(es) did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? Einstein used an identity from his assumed linear coordinate covariance x'= Mx to relate i…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar fields are usually not canonical, which makes analytic treatment difficult. Here we investigate under what conditions the theories can be transformed to the quasi-canonical form, in which case the effective metric tensor in field space is conformally flat. We solve the relevant nonlinear partial differential equations for arbitrary number of scalar fields an…
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