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1.
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
2.
Michael Keyl 《International Journal of Theoretical Physics》1998,37(1):375-385
The major subject of algebraic quantum fieldtheory is the study of nets of local C*-algebras, i.e.,maps
(
) assigning to each open,relatively compact region of space-time (M, g) aC*-algebra
(
), whose self-adjoint elements describe localobservables measurable in the region
. A question discussed recently in a number ofpapers is how much information about the geometricstructure of the underlying space-time (M, g) is encoded in the algebraicstructure of the net
(
). Followingthese ideas, it is demonstrated in this paper howspace-time-related concepts like causality and observerscan be described in a purely algebraic way, i.e., using only thelocal algebras
(
).These results are then used to show how the space-time(M, g) can be reconstructed from the set
loc := {
(
)|
M open,
compact} of local algebras. 相似文献
3.
C. Quesne 《International Journal of Theoretical Physics》1999,38(7):1905-1923
GLh(n) ×GLh(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras
are built in terms of thecorresponding Rh and
-matrices by contracting theGLq(n) ×
-covariant q-bosonic (or q-fermionic) algebras
, = 1, 2.When using a basis of
wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra Uq(gl(n))
, a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingUh(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some Uh(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of
(2, 1). 相似文献
4.
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
5.
The CPT Group of the Dirac Field 总被引:2,自引:2,他引:0
Miguel Socolovsky 《International Journal of Theoretical Physics》2004,43(9):1941-1967
Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields
,
and
, where
and
. These sets are given by
,
,
and
,
,
. Then
, and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively,
and
, which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that
and
, where
is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of
by
, isomorphic to a semidirect product of these groups; S6 and S8 are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group
, which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with
, which is then called the matrix CPT group. It turns out that
, where
is the dicyclic group of 8 elements and S10 is the symmetric group of 10 elements. Since
, the quaternion group, and
, the 0-sphere, then
. 相似文献
6.
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
7.
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
8.
Richard L. Liboff 《International Journal of Theoretical Physics》2002,41(10):1957-1970
Three problems related to the spherical quantum billiard in
are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in
. The second topic addresses the first-excited-state theorem for the spherical quantum billiard in
. Wavefunctions for this system are given by the product form, (
)Z
q+()Y
(n)
, where is dimensionless displacement,
is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written
. It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in
is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in
. In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in
by enumerating independent degenerate product eigenstates of the Laplacian. 相似文献
9.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
10.
In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators
. The reduction of the Poisson structure to the symplectic submanifold
gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as
, where
means the multiplicity of roots and to the case (b) is defined by
where
is the multiplicity of poles. We prove that
-algebra is isomorphic via a transformation to
U(1) with m=
. We also give the explicit free fields representations for these W-algebras. 相似文献
11.
We consider solutions to the Dirac equation in the presence of an external axial vector potential
coupled to the spinor field psi through the interaction term
. There turn out to be no bound-state energies in this system consistent with a normalizable wave function. 相似文献
12.
The product of two real spectral triples
and
, the first of which is necessarily even, was defined by A.Connes as
given by
and, in the even-even case, by
. Generically it is assumed that the real structure
obeys the relations
,
,
, where the
-sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes'
>-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this
-sign table. In this Letter, we propose an alternative definition of the product real structure such that the
-sign table is also satisfied by the product. 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 zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that
being the height of the current algebra representation) acts in
-dimensional indefinite metric space
of quantum group invariant vectors. The generalized cohomologies Ker
are 1-dimensional. Their direct sum spans the physical subquotient of
. 相似文献
15.
Hyperbolic Conformal Geometry with Clifford Algebra 总被引:4,自引:0,他引:4
Hongbo Li 《International Journal of Theoretical Physics》2001,40(1):81-94
In this paper, we study hyperbolic conformal geometry following a Clifford algebraic approach. Similar to embedding an affine space into a one-dimensional higher linear space, we embed the hyperboloid model of the hyperbolic n-space in
into
. The model is convenient for the study of hyperbolic conformal properties. Besides investigating various properties of the model, we also study conformal transformations using their versor representations. 相似文献
16.
The spaces of linear differential operators
acting on -densities on
and the space
of functions on
which are polynomial on the fibers are not isomorphic as modules over the Lie algebra Vect (n) of vector fields of n. However, these modules are isomorphic as sl(n + 1,)-modules where
is the Lie algebra of infinitesimal projective transformations. In addition, such an
-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the
-equivariant symbol map to study the
of kth-order linear differential operators acting on -densities, for an arbitrary manifold M and classify the quotient-modules
. 相似文献
17.
Stefano De Leo Waldyr A. Rodrigues Jayme Vaz 《International Journal of Theoretical Physics》1998,37(9):2415-2431
Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit
. We discuss two possibilities which appearin the multivector algebra approach: the123 and 21 complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit
is also discussed. 相似文献
18.
We consider the Dirichlet Laplacian for astrip in
with one straight boundary and a width
, where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase,
, the operator has nobound statesfor small
.On the otherhand, a weakly bound state existsprovided
. In thatcase, there are positive c
1,c
2 suchthat the corresponding eigenvalue satisfies
for all
sufficiently small. 相似文献
19.
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
20.
Let (M, g) be a pseudo-Riemannian manifold and
the space of densities of degree on M. Denote
the space of differential operators from
to
of order k and S
k
with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map
. This result generalizes that of Duval and Ovsienko. 相似文献