Han-Ying Guo, Chao-Guang Huang, Hong-Tu Wu, Bin Zhou
Based on the principle of relativity and the postulate on universal invariant constants (c,l), all possible kinematics can be set up with sub-symmetries of the Umov-Weyl-Fock transformations for the inertial motions. Further, in the combinatory approach, all these symmetries are intrinsically related to each other, e.g. to the very important dS kinematics for the cosmic scale physics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
I give a brief review on motivations, basic postulates, and recent developments in Doubly Special Relativity Theory.
We argue that recently proposed by Amelino-Camelia et all [1,2] so-called doubly special relativity (DSR), with deformed boost transformations identical with the formulae for $κ$-deformed kinematics in bicrossproduct basis is a classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed fourmomenta as advocated in [1, 2] implies that DSR is obtained by considering nonlinear fourmomenta basis of classical Poincaré algebra and it does not lead to noncommutative space-time. We also show how to construct large two classes of doubly special relativity th…
In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity that preserves the …
It is discussed whether some of the consistency problems of present-day physics could be solved by replacing special relativity, whose underlying kinematics is ruled by the Poincare' group, by de Sitter relativity, with underlying kinematics ruled by the de Sitter group. In contrast to ordinary special relativity, which seems to fail at the Planck scale, this new relativity is "universal" in the sense that it holds at all energy scales.
A space of kinematic quantum states for the Teleparallel Equivalent of General Relativity is constructed by means of projective techniques. The states are kinematic in this sense that their construction bases merely on the structure of the phase space of the theory and does not take into account constraints on it. The space of quantum states is meant to serve as an element of a canonical quantization of the theory.
Phonons mimicking doubly special relativity kinematics
本文通过设计流体相互作用势，构造了两个流体动力学模型，使声子模拟双重狭义相对论运动学，并展示了弹性储存与恢复力分别对应 Amelino-Camelia 和 Magueijo-Smolin 模型。
Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincaré invariance that preserves the Poincaré algebra, and only modifies its action on phase space in a Lorentz-invariant way. We show that, in contrast to the case where the Poincaré algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We give some nontrivial examples of this arising from doubly special relativity and noncommutative geometry and show that Hopf-algebra m…
Gravitational wave polarization modes and the kinematical tensors in general relativity and beyond
本文研究了引力波极化模式与运动学张量（膨胀、剪切和涡旋）之间的关系，通过自由下落测试粒子分析了广义相对论及其他度量引力理论中的关联，揭示了剪切的横向分量与张量极化模式、膨胀与横纵极化模式以及剪切和涡旋的横纵分量与矢量极化模式之间的联系。
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert spac…
Doubly special relativity has been studied for the last twenty years as a way to go beyond the special relativistic kinematics, trying to capture residual effects of a quantum gravity theory. In particular, in doubly special relativity the Einstenian relativity principle is generalized, adding to the speed of light another relativistic invariant, the Planck energy. There are several papers in the literature showing a connection between this deformed kinematics and a curved momentum space. Here we review how such kinematics can be derived from geometrical ingredients in a rigorous way, and how …
This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of excluding unphysical predictions of relativity theories thanks to the use of the concept of the maximum velocity of the observed motion of objects. It proposes a model of a vacuum-like medium with a kinematical property of relativistically invariant rest. The Planck quantities are considered as fundamental physical constants related to the structure of this mediu…
One important discovery in recent years is that the total amplitude of gauge theory can be written as BCJ form where kinematic numerators satisfy Jacobi identity. Although the existence of such kinematic numerators is no doubt, the simple and explicit construction is still an important problem. As a small step, in this note we provide an algebraic approach to construct these kinematic numerators. Under our Feynman-diagram-like construction, the Jacobi identity is manifestly satisfied. The corresponding color ordered amplitudes satisfy off-shell KK-relation and off-shell BCJ relation similar to…
I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkowski space, rigid motion (the Noether-Herglotz theorem), and the geometry of rotating reference frames. Representation-theoretic aspects of the Lorentz group are not included. A series of appendices present some related mathema…
Starting from noncommutative generalization of Minkowski space we consider quantum deformed relativistic symmetries which lead to the modification of kinematics of special relativity. The noncommutative field theory framework described by means of the star product formalism is briefly described. We briefly present the quantum modifications of Einstein gravity
There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar $\mathcal{N}=4$ SYM. A long standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction al…
We propose that the symbol alphabet for classes of planar, dual-conformal-invariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of) $G_+(4,n)/T$ for the $n$-particle massless kinematics. For one-, two-, three-mass-easy hexagon kinematics with $n=7,8,9$, we find finite cluster algebras $D_4$, $D_5$ and $D_6$ respectively, in accordance with previous result on alphabets of these integrals. As the main example, we consider hexagon kinematics with two massive corners on opposite sides and find a …
The Poincare' group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincare' as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of the cosmological constant and to explain the cosmic coincidence. When applied to the propagation of ultra-high en…
We encode dynamical symmetries of Born-Infeld theory in a geometry on the tangent bundle of generally curved spacetime manifolds. The resulting covariant formulation of a maximal acceleration extension of special and general relativity is put to use in the discussion of particular point particle dynamics and the transition to a first quantized theory.
The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter spacetime. The basic conclusion is that it is possible to have an invariant length parameter without breaking the Lorentz symmetry. This result may have important implications for the study of quantum kinematics, and in particular for quantum gravity.
We discuss a way to obtain the doubly special relativity kinematical rules (the deformed energy-momentum relation and the nonlinear Lorentz transformations of momenta) starting from a singular Lagrangian action of a particle with linearly realized SO(1,4) symmetry group. The deformed energy-momentum relation appears in a special gauge of the model. The nonlinear transformations of momenta arise from the requirement of covariance of the chosen gauge.
Dynamical symmetries of Born-Infeld theory associated with its maximal field strength are encoded in a geometry on the tangent bundle of spacetime manifolds. The resulting extension of general relativity respecting a finite upper bound on accelerations is put to use in the discussion of particle dynamics, first quantization, and the derivation of a correction to the Thomas precession.
Doubly special relativity as a non-local quantum field theory
本文基于几何解释将双狭义相对论构造为无穷阶导数的非局域量子场论，限制模型须保持线性 Lorentz 不变性，量子化场并导出变形 Maxwell 方程，比较不同动量空间中场的原点发散行为。
Since the appearance of Einstein's paper {\em"On the Electrodynamics of Moving Bodies"} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell's equations. The celebrated mass-energy equivalence relation, $E=mc^2$, is derived by Einstein using thought experiments involving the kinematics of the emission of light (electromagnetic energy) and the relativity principle. Text book derivations often follow paths similar to Einstein's, or the analysis of the kinematics of particle collisions interpreted from the perspective of different inertial frame…
This article is an extension of the author's second master thesis [1]. It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a g…
In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics.
De Sitter-invariant approach to cosmology
本文提出德西特不变狭义相对论以解决普朗克长度与洛伦兹不变性的冲突，并推导出德西特不变广义相对论下的弗里德曼方程，探讨其对宇宙学的影响。
We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and focuses mainly on the observables over field configurations, given by certain spaces of functionals which are studied here in depth. The analysis of such functionals is characterized by a combination of geometric, analytic and algebraic elements which (1) make our approach closer to quantum field theory, (2) allow for a rigorous analytic refinement of many computational formulae from the functional formulat…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local kinematic Hilbert spaces. In this paper, we consider a theory of quantum gravity that does not come with a preferred partitioning of the kinematic Hilbert space. It is pointed out that, in such a theory, dimension, signature, topology and geometry of spacetime depend on how a collection of local clocks is chosen within the kinematic Hilbert space.
Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincaré invariant Einstein special relativity by a de Sitter invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called 'de Sitter modified general relativity'. In this paper, the Newtonian limit of this theory is us…
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of non-linear, diffeomorphism invariant theories such as general relativity. Recently, an extension of the required type was proposed by one of us using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples. The choice of examples and some of the …
In the presence of a cosmological constant, ordinary Poincare' special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the ordinary notions of energy and momentum change, and will satisfy a different kinematic relation. Such a theory is a different kind of a doubly special relativity. Since the only difference between the Poincare' and the de Sitter groups is the replacement of translations by certain linear combinations of translations and proper conformal transformations, the …
We show that Dirac-Born-Infeld theory possesses a hidden invariance that enhances the local O(1,p) Lorentz symmetry on a Dirichlet p-brane to an O(1,p) x O(1,p) gauge group, encoding both an invariant velocity and acceleration (or length) scale. This enlarged gauge group predicts consequences for the kinematics of observers on Dirichlet branes, with admissible accelerations being bounded from above. An important lesson beyond string theory is that a fundamental length scale can be implemented into the kinematics of general relativity, whilst preserving both space-time as a smooth manifold and …
An algebraic formulation of general relativity is proposed. The formulation is applicable to quantum gravity and noncommutative space. To investigate quantum gravity we develop the canonical formalism of operator geometry, after reconstructing an algebraic canonical formulation on analytical dynamics. The remarkable fact is that the constraint equation and evolution equation of the gravitational system are algebraically unified. From the discussion of regularization we find the quantum correction of the semi-classical gravity is same as that already known in quantum field theory.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。