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1.
Marcus Pivato 《Journal of statistical physics》2003,110(1-2):247-267
If
, and
is a finite (nonabelian) group, then
is a compact group; a multiplicative cellular automaton (MCA) is a continuous transformation
which commutes with all shift maps, and where nearby coordinates are combined using the multiplication operation of
. We characterize when MCA are group endomorphisms of
, and show that MCA on
inherit a natural structure theory from the structure of
. We apply this structure theory to compute the measurable entropy of MCA, and to study convergence of initial measures to Haar measure. 相似文献
2.
It is shown that solvable mixed spin ladder models can be constructed from su(N) permutators. Heisenberg rung interactions appear as chemical potential terms in the Bethe Ansatz solution. Explicit examples given are a mixed spin-
spin-1 ladder, a mixed spin-
spin-
ladder and a spin-1 ladder with biquadratic interactions. 相似文献
3.
Stefano De Leo Zbigniew Oziewicz Waldyr A. Rodrigues Jayme Vaz 《International Journal of Theoretical Physics》1999,38(9):2349-2369
We formulate the variational principle of theDirac equation within the noncommutative even space-timesubalgebra, the Clifford
-algebra
. A fundamental ingredient in ourmultivectorial algebraic formulation is a
-complex geometry,
. We derive the Lagrangian for theDirac-Hestenes equation and show that it must be mapped on
, where denotes an
-algebra of functions. 相似文献
4.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
5.
Let
be the Haag--Kastler net generated by the
(2) chiral current algebra at level 1. We classify the SL(2,
)-covariant subsystems
by showing that they are all fixed points nets
H
for some subgroup H of the gauge automorphisms group SO(3) of
. Then, using the fact that the net
1 generated by the
(1) chiral current can be regarded as a subsystem of
, we classify the subsystems of
1. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem
. 相似文献
6.
Let
be von Neumann algebras acting on a Hilbert space
and let
be a common cyclic and separating vector. We say that
have the modular intersection property with respect to
if(1)
-half-sided modular inclusions,(2)
(If (1) holds the strong limit exists.) We show that under these conditions the modular groups of
and
generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2,
)/Z
2 generated by modular groups. 相似文献
7.
P. C. Hemmer 《Journal of statistical physics》2000,100(1-2):3-11
A binary mixture of long rigid rods of diameters D
i and lengths L
i (i=1, 2) may demix into two isotropic phases, and we give necessary conditions on the molecular size parameters for this transition to exist. These conditions imply that the two diameters must be sufficiently unequal, D
2/D
1>(
+
)2, or D
2/D
1<(
+
)2, while the length ratio is limited to an interval f
–(D
2/D
1)<L
2/L
1<f
+(D
2/D
1). The functions f
± are given explicitly. 相似文献
8.
Stan Gudder 《Foundations of Physics》1999,29(6):877-897
This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the -effect algebra of effects (fuzzy events)
and the set of probability measures
on a measurable space
. An observable
is defined, where
is the value space of X. It is noted that there exists a one-to-one correspondence between states on
and elements of
and between observables
and -morphisms from
to
. Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map
is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. 相似文献
9.
Let X be a connected Riemann surface equipped with a projective structure
. Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using
, this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using
, a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed. 相似文献
10.
We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation
, with initial data
. We assume that the coefficient
is real, bounded and slowly varying function, such that
, where
. We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space
. In comparison with the previous paper (Internat. Res. Notices
8 (1999), 395–418), here we exclude the condition that the integral of the initial data u
0 is zero. We prove the time decay estimates
and
for all
, where
. We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution. 相似文献
11.
Mauro Napsuciale 《Foundations of Physics》2003,33(5):741-768
In this work we review the derivation of Dirac and Weinberg equations based on a principle of indistinguishability for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields
equations of motion for any representation containing spin j and lower spins. We also use the obtained generators of the HLG for a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j=
, there exists no Dirac-like equation for the (j,0)(0,j) representation nor for the (
,
) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)(
,
)(0,1) representation by this method and show that the (1,
)(
,1) representation satisfies a Dirac-like equation which describes a multiplet of
with masses m and m/2, respectively. 相似文献
12.
A simplified construction of representations is presented for the quantized enveloping algebra
q (
), with
being a simple complex Lie algebra belonging to one of the four principal series A\ell, B\ell, C\ell or D\ell. The carrier representation space is the quantized algebra of polynomials in antiholomorphic coordinate functions on the big cell of a coadjoint orbit of K where K is the compact simple Lie group with the Lie algebra
– the compact form of
. 相似文献
13.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group
in the following manner. There is a partition
into disjoint subsets and a bijection between
and the sectors
of the (p,q)-minimal model such that the fusion rules
correspond to
where
. 相似文献
14.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups
q(gl(2N+1)) is constructed as a twisting of the universal R-matrix
S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle
is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's
(N)
q (gl(2N+1))), providing the factorization property of
. As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo. 相似文献
15.
V. Gaftoi J. Lopez-Bonilla G. Ovando 《International Journal of Theoretical Physics》1999,38(3):939-943
Weert found a superpotential
for the bounded part of the Maxwelltensor
associatedto the Lienard–Wiechert field. Here we obtain afourth-rank generator
for the superpotential
. 相似文献
16.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
17.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
18.
J. Donin 《Czechoslovak Journal of Physics》1997,47(11):1115-1122
For
we construct a two parametric
-invariant family of algebras,
, that is a quantization of the function algebra
on the coadjoint representation. Along the parameter t the family gives a quantization of the Lie bracket. This family induces a two parametric
-invariant quantization on the maximal orbits, which includes a quantization of the Kirillov-Kostant-Souriau bracket. Yet we construct a quantum de Rham complex on
. 相似文献
19.
A locally finite, causal, and quantal substitute for a locally Minkowskian principal fiber bundle
of modules of Cartan differential forms over a bounded region X of a curved C
-smooth spacetime manifold M with structure group G that of orthochronous Lorentz transformations L
+ := SO(1,3), is presented.
is usually regarded as the kinematical structure of classical Lorentzian gravity when the latter is viewed as a Yang-Mills type of gauge theory of a sl(2, {})-valued connection 1-form
. The mathematical structure employed to model this replacement of
is a principal finitary spacetime sheaf
of quantum causal sets
with structure group G
n, which is a finitary version of the continuous group G of local symmetries of General Relativity, and a finitary Lie algebra g
n-valued connection 1-form
on it, which is a section of its subsheaf
.
is physically interpreted as the dynamical field of a locally finite quantum causality, whereas its associated curvature
as some sort of finitary and causal Lorentzian quantum gravity. 相似文献
20.
The authors deal with the tunneling of electrons across an inhomogeneous delta-barrier defined by the potential energy
(where
0$$
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and
0$$
" align="middle" border="0">
are two constants). In particular, the perpendicular incidence of an electron with a given value
of the wave vector
is considered. The electron is forward-scattered into the region behind the barrier (region 2:
0$$
" align="middle" border="0">
), i. e. the wave function
is composed of plane waves with all wave vectors
such that
and
\left. 0 \right)} $$
" align="middle" border="0">
) (where
). Therefore, if
0$$
" align="middle" border="0">
, the wave function of the electron is represented as
, where
. An approximate formula is derived for the amplitude
. The authors pay a special attention to the flow density
and calculate this function in two cases: 1. for the plane
and 2. for high values of
is the diffraction angle). The authors discuss the relevance of their diffraction problem in a prospective quantum-mechanical theory of the tunneling of electrons across a randomly inhomogeneous Schottky barrier. 相似文献