Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopole-like field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. It generalizes the fine-tuned inverse-square plus Coulomb potential, found before by McIntosh and Cisneros, and by Zwanziger, for a charged particle in the field of a Dirac monopole. Following Fehér, the result is interpreted as describing motion in the asymptotic field of a self-dual Prasad-Sommerfield monopole. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere and Wilczek, a conserved angular momentum is constructed, despite the non-conservation of the electric charge. No Runge-Lenz vector has been found.
Infinite sequence of new conserved quantities for N=1 SKdV and the supersymmetric cohomology
得到了N=1 Super KdV（SKdV）方程的一个新的非定域守恒量的无穷序列.序列的构建，通过加德纳变换，从一个新的守恒量的超级加德纳方程。超对称生成元定义了从所有守恒量的空间到自身的幂零运算。在$C_\downarrow^\infty$超场环上，局部守恒量是封闭的，但不是精确的。然而，在$C_{NL,1}^\infty$超场的环上，$C_\downarrow^\infty$环的扩展，它们变得精确并且等于适当权重的奇非局部守恒量子集的SUSY变换。其余的奇非定域守恒量生成封闭的几何对象，当环扩展到$C_{NL,2}^\infty$超场时，这些封闭的几何对象变得精确，并且等于我们得到的新的偶非定域守恒量的SUSY变换。这些方程完全符合已知守恒量的超对称上同调。
We consider a class of theories with unfree gauge symmetry, whose gauge parameters are restricted by differential equations. We demonstrate that such theories admit global conserved quantities, whose on-shell values are defined by asymptotics of the fields rather than Cauchy data. The global conserved quantities can be deduced proceeding from the equations restricting gauge parameters, and they are treated differently by two BRST complexes corresponding to a system with unfree gauge symmetry.
The thermodynamic quantities such as the local temperature, heat capacity, off-shell free energy and the stability of a black hole involving a global monopole within or outside the $f(R)$ gravity are examined. We compare the two classes of results to show the influence from the generalization of the general relativity. It is found that the $f(R)$ theory will modify the thermodynamic properties of black holes, but the shapes of curves for thermodynamic quantities with respect to the horizon are similar to the results within the frame of general relativity. In both cases there will exist a small…
We obtain an infinite sequence of bosonic non-local conserved quantities for the N=1 supersymmetric Korteweg-de Vries equation. It is generated from a bosonic non-local conserved quantity of Super Gardner equation. In distinction to the already known one with odd parity and dimension 1/2, it has even parity and dimension 1. It fits exactly in the supersymmetric cohomology in the space of conserved quantities that we also introduce here. Using results from this cohomology we obtain the Poisson bracket of several non-local conserved quantities, including the already known odd ones and the new ev…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.
We revisit the thermodynamic aspects of the scalar-tensor theory of gravity in the Jordan and in the Einstein frame. Examining the {\it missing links} of this theory carefully, we establish the thermodynamic descriptions from the conserved currents and potentials by following both the Noether and the Abbott-Deser-Tekin (ADT) formalism. With the help of conserved Noether current and potential, we define the thermodynamic quantities, which we show to be {\it conformally invariant}. Moreover, the defined quantities are shown to fit nicely in the laws of (the first and the second) black hole therm…
In 2+1-dimensional conformal field theories with a global U(1) symmetry, monopoles can be introduced through a background gauge field that couples to the U(1) conserved current. We use the state-operator correspondence to calculate scaling dimensions of such monopoles. We obtain the next-to-leading term in the 1/N_b expansion of the Wilson-Fisher fixed point in the theory of N_b complex bosons.
The identification between the bulk and boundary conserved quantities
Central South University of Forestry and Technology（中南林业科技大学）；Beijing Normal University（北京师范大学）；Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）
We study physical properties of constant curvature black holes (CCBHs) in Einstein anti-de Sitter (AdS) gravity. These objects, which are locally AdS throughout the space, are constructed from identifications of global AdS spacetime, in a similar fashion as Banados-Teitelboim-Zanelli (BTZ) black hole in three dimensions. We find that, in dimensions equal or greater than four, CCBHs have zero mass and angular momentum. Only in odd dimensions we are able to associate a nonvanishing conserved quantity to these solutions, which corresponds to the vacuum (Casimir) energy of the spacetime.
For field theories in which no small parameter is available, we propose a definition of nonperturbative quantum states in terms of the complete set of Green functions, based upon the utilization of Heisenberg's quantization procedure. We apply this method to obtain the energy spectra of a quantum monopole and of a flux tube. The partition function and thermodynamic quantities for one quantum monopole are evaluated numerically. A dilute gas of noninteracting quantum monopoles is considered, for which the partition function and thermodynamic quantities are evaluated as well. All the obtained sta…
We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analogue of holographic charges at future and past infinity and at other Cauchy surfaces $I_t$ as integrals over the intersection of timelike surfaces $C$ and the Cauchy surface $I_t$. In general, the charges $Q^t$ defined on the Cauchy surface $I_t$ depend on $C$, but if gravitational flux is absent the charges are independent of $C$. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by $C_1, C_2$ and two Cauchy surfaces the…
We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effcetive values of mass and angular momentum are then used to derive an identity ($K_{χ^μ}=2ST$) which relates the Komar conserved charge ($K_{χ^μ}$) corresponding to the null Killing vector ($χ^μ$) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of …
In this paper we generalize the off-shell Abbott-Deser-Tekin (ADT) conserved charge formalism to Palatini theory of gravity with torsion and non-metricity. Our construction is based on the coordinate formalism and the independent dynamic fields are the metric and the affine connection. For a general Palatini theory of gravity, which is diffeomorphism invariant up to a boundary term, we obtain the most general expression for off-shell ADT potential. As explicit examples, we derive the off-shell ADT potentials for Einstein-Hilbert action, the most general $L(g_{μν}, R^λ{}_{ναμ}, T^λ{}_{αβ}, Q_{α…
Motivated by the recent work on critical gravity theories in dimensions D>3, we reexamine the results in [arXiv:hep-th/0501044], where the conformal mass definition of Ashtekar, Magnon and Das (AMD) for asymptotically AdS space-times was generalized to incorporate curvature squared terms. The results in [arXiv:hep-th/0501044] appear to contradict the findings in critical gravity, where, using the methods of Deser and Tekin, black holes were shown to have zero mass. We show that after correcting an error in [arXiv:hep-th/0501044], the AMD approach actually produces results in complete agreement…
We derive conservation laws from interactions of actively-interacting braid-like excitations of embedded framed spin networks in Quantum Gravity. Additionally we demonstrate that actively-interacting braid-like excitations interact in such a way that the product of interactions involving two actively-interacting braid-like excitations produces a resulting actively-interacting form.
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents that characterize spontaneous flows in the system. In this work, we consider quantum many-body systems on a finite one-dimensional lattice and discuss the scaling of the persistent currents as a function of the system size. We show that, when the conserved quantities are given as the Noether charges associated with internal symmetries or the Hamiltonian itself…
We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar-tensor models, we show that the Hojman conserved quantities exist for a wide range of V(ϕ)-potentials and allow to find exact solutions for the cosmic scale f…
We show that the subregion entanglement Hamiltonians of excited eigenstates of a quantum many-body system are approximately linear combinations of subregionally (quasi)local approximate conserved quantities, with relative commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can obtain these conserved quantities as the EHSM eigen-operators with nonzero eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues is c…
