共查询到20条相似文献,搜索用时 31 毫秒
1.
T. Mei 《General Relativity and Gravitation》2008,40(9):1913-1945
Both the Einstein–Hilbert action and the Einstein equations are discussed under the absolute vierbein formalism. Taking advantage
of this form, we prove that the “kinetic energy” term, i.e., the quadratic term of time derivative term, in the Lagrangian
of the Einstein–Hilbert action is non-positive definitive. And then, we present two groups of coordinate conditions that lead
to positive definitive kinetic energy term in the Lagrangian, as well as the corresponding actions with positive definitive
kinetic energy term, respectively. Based on the ADM decomposition, the Hamiltonian representation and canonical quantization
of general relativity taking advantage of the actions with positive definitive kinetic energy term are discussed; especially,
the Hamiltonian constraints with positive definitive kinetic energy term are given, respectively. Finally, we present a group
of gauge conditions such that there is not any second time derivative term in the ten Einstein equations. 相似文献
2.
D.M. Gitman V.G. Kupriyanov 《The European Physical Journal C - Particles and Fields》2008,54(2):325-332
It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them
θ-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of
such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding
field theory. In the present article, we discuss the problem of constructing θ-modified actions for relativistic QM. We construct
such actions for relativistic spinless and spinning particles. The key idea is to extract θ-modified actions of the relativistic
particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the
Klein–Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral
representations. Effective actions in such representations we treat as θ-modified actions of the relativistic particles. To
confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein–Gordon and Dirac equations in
the noncommutative field theories. The θ-modified action of the relativistic spinning particle is just a generalization of
the Berezin–Marinov pseudoclassical action for the noncommutative case. 相似文献
3.
In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as nonassociative strict deformation quantization of ordinary principal torus bundles. We then relate this to T-duality of principal torus bundles with H-flux. In particular, the Octonions fit nicely into our theory. 相似文献
4.
In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton–Jacobi method.
The integrablity conditions are considered on the equations of motion and the action function as well in order to obtain the
path integral quantization of singular Lagrangians with linear velocities. 相似文献
5.
Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2 + 1 dimensions through a linking gauge theory that ensures dynamical equivalence with General Relativity. The Hamiltonian we obtain is formally a reduced phase space Hamiltonian. The construction of the Shape Dynamics Hamiltonian on higher genus surfaces is not explicitly possible, but we give an explicit expansion of the Shape Dynamics Hamiltonian for large CMC volume. The fact that all local constraints are linear in momenta allows us to quantize these explicitly under a certain assumption on the kinematic Hilbert space, and the quantization problem for Shape Dynamics turns out to be equivalent to reduced phase space quantization. We consider the large CMC-volume asymptotics of conformal transformations of the wave function. We then discuss the similarity of Shape Dynamics on the 2-torus with the explicitly constructible strong gravity Shape Dynamics Hamiltonian in higher dimensions. 相似文献
6.
Hideki Omori Yoshiaki Maeda Naoya Miyazaki Akira Yoshioka 《Letters in Mathematical Physics》2007,82(2-3):153-175
We propose suitable ideas for non-formal deformation quantization of Fréchet Poisson algebras. To deal with the convergence
problem of deformation quantization, we employ Fréchet algebras originally given by Gel’fand–Shilov. Ideas from deformation
quantization are applied to expressions of elements of abstract algebras, which leads to a notion of “independence of ordering
principle”. This principle is useful for the understanding of the star exponential functions and for the transcendental calculus
in non-formal deformation quantization.
Akira Yoshioka was partially supported by Grant-in-Aid for Scientific Research (#19540103.), Ministry of Education, Science
and Culture, Japan. 相似文献
7.
G.M. von Hippel M.N.R. Wohlfarth 《The European Physical Journal C - Particles and Fields》2006,47(3):861-872
We present a manifestly covariant quantization procedure based on the de Donder–Weyl Hamiltonian formulation of classical
field theory. This procedure agrees with conventional canonical quantization only if the parameter space is d=1 dimensional
time. In d>1 quantization requires a fundamental length scale, and any bosonic field generates a spinorial wave function,
leading to the purely quantum-theoretical emergence of spinors as a byproduct. We provide a probabilistic interpretation of
the wave functions for the fields, and we apply the formalism to a number of simple examples. These show that covariant canonical
quantization produces both the Klein–Gordon and the Dirac equation, while also predicting the existence of discrete towers
of identically charged fermions with different masses. Covariant canonical quantization can thus be understood as a “first”
or pre-quantization within the framework of conventional QFT.
PACS 04.62.+v; 11.10.Ef; 12.10.Kt 相似文献
8.
Oliver Knill 《Communications in Mathematical Physics》1999,204(1):85-88
We note that every finite or infinite dimensional real-analytic Hamiltonian system with a quasi-periodic invariant KAM torus
of finite dimension d≥ 2 can be perturbed in such a way that the new real-analytic Hamiltonian system has a weakly mixing invariant torus of the
same dimension.
Received: 24 April 1998/ Accepted: 14 January 1999 相似文献
9.
We use the decomposition of o(3, 1) = sl(2; ℂ)1 ⊕sl(2; ℂ)2 in order to describe nonstandard quantum deformation of o(3, 1) linked with Jordanian deformation of sl(2; ℂ). Using the
twist quantization technique, we obtain the deformed coproducts and antipodes, which can be expressed in terms of real physical
Lorentz generators. We describe the extension of the considered deformation of D = 4 Lorentz algebra to the twist deformation of D = 4 Poincare algebra with dimensionless deformation parameter.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
10.
We consider infinite dimensional Hamiltonian systems. We prove the existence of “Cantor manifolds” of elliptic tori–of any
finite higher dimension–accumulating on a given elliptic KAM torus. Then, close to an elliptic equilibrium, we show the existence
of Cantor manifolds of elliptic tori which are “branching” points of other Cantor manifolds of higher dimensional tori. We
also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along
a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization
of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear
wave equation. 相似文献
11.
We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative
structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local
fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit
formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also
via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski
space.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.
Presented by J. Lukierski. 相似文献
12.
The mathematical framework for an exact quantization of the two-dimensio‐nal coset space σ-models coupled to dilaton gravity,
that arise from dimensional reduction of gravity and supergravity theories, is presented. Extending previous results [49]
the two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the isomonodromic
sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions
of the corresponding Wheeler–DeWitt equations to solutions of a modified (Coset-)Knizhnik-Zamolodchikov system.
Received: 25 July 1996 / Accepted: 23 April 1997 相似文献
13.
14.
Philip D. Mannheim 《Foundations of Physics》2007,37(4-5):532-571
We present a solution to the ghost problem in fourth order derivative theories. In particular we study the Pais–Uhlenbeck
fourth order oscillator model, a model which serves as a prototype for theories which are based on second plus fourth order
derivative actions. Via a Dirac constraint method quantization we construct the appropriate quantum-mechanical Hamiltonian
and Hilbert space for the system. We find that while the second-quantized Fock space of the general Pais–Uhlenbeck model does
indeed contain the negative norm energy eigenstates which are characteristic of higher derivative theories, in the limit in
which we switch off the second order action, such ghost states are found to move off shell, with the spectrum of asymptotic
in and out S-matrix states of the pure fourth order theory which results being found to be completely devoid of states with
either negative energy or negative norm. We confirm these results by quantizing the Pais–Uhlenbeck theory via path integration
and by constructing the associated first-quantized wave mechanics, and show that the disappearance of the would-be ghosts
from the energy eigenspectrum in the pure fourth order limit is required by a hidden symmetry that the pure fourth order theory
is unexpectedly found to possess. The occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure fourth order
theories per se, but rather to be one which only arises when fourth and second order theories are coupled to each other. 相似文献
15.
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A–model). The second theory is an intermediate model, which we call the I–model. The equivalence between the A–model and the I–model is achieved by realizing the former as a deformation of a linear sigma model with a complex torus as the target and then applying to it a version of the T–duality. On the other hand, the I–model is closely related to the twisted Landau-Ginzburg model (the B–model) that is mirror dual to the A–model. Thus, the mirror symmetry is realized in two steps, via the I–model. In particular, we obtain a natural interpretation of the superpotential of the Landau-Ginzburg model as the sum of terms corresponding to the components of a divisor in the toric variety. We also relate the cohomology of the supercharges of the I–model to the chiral de Rham complex and the quantum cohomology of the underlying toric variety.Partially supported by the DARPA grant HR0011-04-1-0031 and the NSF grant DMS-0303529.Partially supported by the Federal Program 40.052.1.1.1112, by the Grants INTAS 03-51-6346, NSh-1999/2003.2 and RFFI-04-01- 00637. 相似文献
16.
We prove that, for the moduli space of flat SU(2)-connections on the 2-dimensional torus, the Weyl quantization and the quantization performed using the quantum group of
SL(2,C) are the same. This is done by comparing the matrices of the operators associated through the two quantizations to cosine
functions. We also discuss the *-product of the Weyl quantization and show that it satisfies the product-to-sum formula for
noncommutative cosines on the noncommutative torus.
Received: 27 January 2002 / Accepted: 9 September 2002 Published online: 19 December 2002
RID="*"
ID="*" Research supported in part by the NSF, award No. DMS 0070690
Communicated by A. Connes 相似文献
17.
T. Skrypnyk 《Czechoslovak Journal of Physics》2002,52(11):1283-1288
We construct a family of infinite-dimensional quasigraded Lie algebras, that could be viewed as deformation of the graded
loop algebras. Using them we obtain new series of integrable Hamiltonian systems on semisimple Lie algebras and their extensions.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. 相似文献
18.
Theodore Voronov 《Communications in Mathematical Physics》1999,205(2):315-336
We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T
⋆
M
is made into a space of (full) symbols of operators acting on forms on M. This gives rise to the composition of symbols, which is a deformation of the (“super”)commutative multiplication of forms.
The symbol calculus is exact for differential operators and the symbols that are polynomial in momenta. We calculate the symbols
of natural Laplacians. (Some nice Weitzenb?ck like identities appear here.) Formulae for the traces corresponding to natural
gradings of Ω (T
⋆
M
) are established. Using these formulae, we give a simple direct proof of the Gauss–Bonnet–Chern Theorem. We discuss these
results in connection with a general question of the quantization of forms on a Poisson manifold.
Received: 12 November 1998 / Accepted: 1 March 1999 相似文献
19.
Yi Lin 《Communications in Mathematical Physics》2008,281(2):469-497
It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized Kähler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes. In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the ${\overline{\partial} \partial}It has been shown recently by Kapustin and Tomasiello that the mathematical notion of Hamiltonian actions on twisted generalized
K?hler manifolds is in perfect agreement with the physical notion of general (2, 2) gauged sigma models with three-form fluxes.
In this article, we study the twisted equivariant cohomology theory of Hamiltonian actions on H-twisted generalized complex manifolds. If the manifold satisfies the -lemma, we establish the equivariant formality theorem. If in addition, the manifold satisfies the generalized K?hler condition,
we prove the Kirwan injectivity in this setting. We then consider the Hamiltonian action of a torus on an H-twisted generalized Calabi-Yau manifold and extend to this case the Duistermaat-Heckman theorem for the push-forward measure.
As a side result, we show in this paper that the generalized K?hler quotient of a generalized K?hler vector space can never
have a (cohomologically) non-trivial twisting. This gives a negative answer to a question asked by physicists whether one
can construct (2, 2) gauged linear sigma models with non-trivial fluxes. 相似文献
20.
Pulak Ranjan Giri 《International Journal of Theoretical Physics》2008,47(10):2583-2590
We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the
Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization,
which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η
2∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since
quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling
anomaly. We also discuss the strong coupling region η
2<0, which supports bound state making the problem re-normalizable. 相似文献