共查询到20条相似文献,搜索用时 31 毫秒
1.
The main goal of this work is to perform a nonholonomic deformation (Fedosov type) quantization of fractional Lagrange–Finsler
geometries. The constructions are provided for a fractional almost K?hler model encoding equivalently all data for fractional
Euler–Lagrange equations with Caputo fractional derivative. 相似文献
2.
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving
a general class of equations including Euler–Poincaré equations on Lie groups and homogeneous spaces. Orbit invariants play
an important role in this context and we use these invariants to prove global existence and uniqueness results for a class
of PDE. This class includes Euler–Poincaré equations that have not yet been considered in the literature as well as integrable
equations like Camassa–Holm, Degasperis–Procesi, μCH and μDP equations, and the geodesic equations with respect to right-invariant Sobolev metrics on the group of diffeomorphisms of
the circle. 相似文献
3.
We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical
equations of motion of the SL(2,ℝ/U(1) theory. We calculate the symplectic structure of this solution by solving a differential
equation of the Gelfand–Dikii type with initial state conditions at infinity, and transform the canonical physical fields
non-locally onto canonical free fields. The results will, finally, be collected in a local B?cklund transformation. These
calculations prepare the theory for an exact canonical quantization.
Received: 9 June 1998 / Accepted: 7 March 1999 相似文献
4.
M. A. Mashkour 《International Journal of Theoretical Physics》1998,37(2):785-797
The canonical formalism of fields consistentwith the covariance principle of special relativity isgiven here. The covariant canonical transformations offields are affected by 4-generating functions. All dynamical equations of fields, e.g., theHamilton, Euler–Lagrange, and other fieldequations, are preserved under the covariant canonicaltransformations. The dynamical observables are alsoinvariant under these transformations. The covariantcanonical transformations are therefore fundamentalsymmetry operations on fields, such that the physicaloutcomes of each field theory must be invariant under these transformations. We give here also thecovariant canonical equations of fields. These equationsare the covariant versions of the Hamilton equations.They are defined by a density functional that is scalar under both the Lorentz and thecovariant canonical transformations of fields. 相似文献
5.
Maxim Dvornikov 《Foundations of Physics》2012,42(11):1469-1479
6.
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
7.
8.
Hans-Christian Herbig Srikanth B. Iyengar Markus J. Pflaum 《Letters in Mathematical Physics》2009,89(2):101-113
We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization,
singularity theory, pp. 443–461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action.
In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic.
We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43–103, 1990) for linear Hamiltonian torus actions.
It follows that reduced spaces of such actions admit continuous star products.
相似文献
9.
D. N. Khan Marwat A. H. Kara F. M. Mahomed 《International Journal of Theoretical Physics》2007,46(12):3022-3029
We show how one can construct conservation laws of equations that are not variational but are Euler–Lagrange in part using Noether-type symmetries associated with partial Lagrangians. These Noether-type symmetries are, usually, not symmetries
of the system. The resultant construction of the conservation law resorts to a formula equivalent to Noether’s theorem. A variety
of examples are given. 相似文献
10.
A discrete version of Lagrangian reduction is developed within the context of discrete time Lagrangian systems on G × G, where G is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of an isotropy subgroup of a fixed element in the representation space of G. Within this context, the reduction of the discrete Euler–Lagrange equations is shown to lead to the so-called discrete Euler–Poincaré equations. A constrained variational principle is derived. The Legendre transformation of the discrete Euler–Poincaré equations leads to discrete Hamiltonian (Lie–Poisson) systems on a dual space to a semiproduct Lie algebra. 相似文献
11.
When using the Dirac hamiltonization of Lagrange systems with constraints, it is convenient to perform a canonical transformation such that the constraints become linear combinations of only a subset of the new variables, while the primary constraints can be identified with some of the variables belonging to this subset. We prove the existence of such canonical transformation, as well as the possibility of separation of first-class constraints.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–97, August, 1983. 相似文献
12.
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
13.
O. S. Zandron 《International Journal of Theoretical Physics》2007,46(11):2758-2773
Starting from a classical 2D superconformal theory described by the Wess–Zumino–Witten action, the canonical exterior formalism
on group manifold for the heterotic supersymmetric sigma model is constructed. The motion equations of the dynamical field
and the constraints are found and analyzed from the geometric point of view. It can be seen how the use of the canonical exterior
formalism is more adequate and simple because of its manifest covariance in all the steps. The relationship between the form
brackets defined in the canonical exterior formalism and the Poisson-brackets is written. Later on, the Dirac-brackets are
written by using the second class constraints provided by the canonical exterior formalism. As it can be seen the canonical
exterior formalism allows to show how the canonical quantization of the heterotic supersymmetric sigma model is facilitated.
Member of the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina. 相似文献
14.
J. Balakrishnan 《The European Physical Journal C - Particles and Fields》2002,23(2):389-395
The method of stochastic quantization of Parisi–Wu is extended to include spinor fields obeying the generalized statistics
of order two consistent with the weak locality requirement. Appropriate Langevin and Fokker–Planck equations are constructed
using paragrassmann variables, which give rise to two fields with different masses in the equilibrium limit, in agreement
with the results of the canonical quantization procedure. The connection between the stochastic quantization method and conventional
Euclidean field theory is established through Klein transformations.
Received: 14 November 2001 / Published online: 8 February 2002 相似文献
15.
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
16.
Roberto Zucchini 《Communications in Mathematical Physics》1997,185(3):723-751
In spite of its simplicity and beauty, the Mathai–Quillen formulation of cohomological topological quantum field theory with
gauge symmetry suffers two basic problems: i) the existence of reducible field configurations on which the action of the gauge group is not free and ii) the Gribov ambiguity associated with gauge fixing, i. e. the lack of global definition on the space of gauge orbits of gauge
fixed functional integrals. In this paper, we show that such problems are in fact related and we propose a general completely
geometrical recipe for their treatment. The space of field configurations is augmented in such a way to render the action
of the gauge group free and localization is suitably modified. In this way, the standard Mathai–Quillen formalism can be rigorously
applied. The resulting topological action contains the ordinary action as a subsector and can be shown to yield a local quantum
field theory,
which is argued to be renormalizable as well. The salient feature of our method is that the Gribov problem is inherent in
localization, and thus can be dealt within a completely equivariant setting, whereas gauge fixing is free of Gribov ambiguities.
For the stratum of irreducible gauge orbits, the case of main interest in applications, the Gribov problem is solvable. Conversely,
for the strata of reducible gauge orbits, the Gribov problem cannot be solved in general and the obstruction may be described
in the language of sheaf theory. The formalism is applied to the Donaldson–Witten model.
Received: 22 July 1996 / Accepted: 21 October 1996 相似文献
17.
H. Nikolić 《The European Physical Journal C - Particles and Fields》2006,47(2):525-529
The covariant canonical method of quantization based on the De Donder–Weyl covariant canonical formalism is used to formulate
a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard non-covariant canonical
quantization, it is necessary to adopt a Bohmian deterministic hidden-variable equation of motion. In this way, string theory
suggests a solution to the problem of measurement in quantum mechanics.
PACS 11.25.-w; 04.60.Ds; 03.65.Ta 相似文献
18.
Shinji Hamamoto 《Zeitschrift fur Physik C Particles and Fields》1983,19(4):353-360
We present a general framework for manifestly-covariant canonical formulation of Poincaré gauge theories. We construct a general class of action that is invariant under two kinds of BRS transformations—translation and internal Lorentz—and suitable for manifestly-covariant canonical quantization. This theory contains a great number of conserved quantities, which we investigate systematically. It is also pointed out that a canonical formulation of higher-derivative theories may be obtained as a limiting case in this framework. 相似文献
19.
The conditions for the existence and stability of cosmological power-law scaling solutions are established when the Einstein–Hilbert
action is modified by the inclusion of a function of the Gauss–Bonnet curvature invariant. The general form of the action
that leads to such solutions is determined for the case where the universe is sourced by a barotropic perfect fluid. It is
shown by employing an equivalence between the Gauss–Bonnet action and a scalar–tensor theory of gravity that the cosmological
field equations can be written as a plane autonomous system. It is found that stable scaling solutions exist when the parameters
of the model take appropriate values. 相似文献
20.
We present the general form of equations that generate a volume-preserving flow on a symplectic manifold M, ) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)H, where H is the corresponding Hamiltonian. 相似文献