50 research outputs found
Physical Vacuum Properties and Internal Space Dimension
The paper addresses matrix spaces, whose properties and dynamics are
determined by Dirac matrices in Riemannian spaces of different dimension and
signature. Among all Dirac matrix systems there are such ones, which nontrivial
scalar, vector or other tensors cannot be made up from. These Dirac matrix
systems are associated with the vacuum state of the matrix space. The simplest
vacuum system realization can be ensured using the orthonormal basis in the
internal matrix space. This vacuum system realization is not however unique.
The case of 7-dimensional Riemannian space of signature 7(-) is considered in
detail. In this case two basically different vacuum system realizations are
possible: (1) with using the orthonormal basis; (2) with using the
oblique-angled basis, whose base vectors coincide with the simple roots of
algebra E_{8}.
Considerations are presented, from which it follows that the least-dimension
space bearing on physics is the Riemannian 11-dimensional space of signature
1(-)& 10(+). The considerations consist in the condition of maximum vacuum
energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio
The BV-algebra structure of W_3 cohomology
We summarize some recent results obtained in collaboration with J. McCarthy
on the spectrum of physical states in gravity coupled to matter. We
show that the space of physical states, defined as a semi-infinite (or BRST)
cohomology of the algebra, carries the structure of a BV-algebra. This
BV-algebra has a quotient which is isomorphic to the BV-algebra of polyvector
fields on the base affine space of . Details have appeared elsewhere.
[Published in the proceedings of "Gursey Memorial Conference I: Strings and
Symmetries," Istanbul, June 1994, eds. G. Aktas et al., Lect. Notes in Phys.
447, (Springer Verlag, Berlin, 1995)]Comment: 8 pages; uses macros tables.tex and amssym.def (version 2.1 or later
Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case
In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact algebras
sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the
fact that they belong to a narrow class of algebras, which we call 'conformal
Lie algebras', which have very similar properties to the conformal algebras of
Minkowski space-time. We give the main multiplets and the main reduced
multiplets of indecomposable elementary representations for n=6, including the
necessary data for all relevant invariant differential operators. In fact, this
gives by reduction also the cases for n<6, since the main multiplet for fixed n
coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text
overlap with arXiv:0812.2690, arXiv:0812.265
On Finite 4D Quantum Field Theory in Non-Commutative Geometry
The truncated 4-dimensional sphere and the action of the
self-interacting scalar field on it are constructed. The path integral
quantization is performed while simultaneously keeping the SO(5) symmetry and
the finite number of degrees of freedom. The usual field theory UV-divergences
are manifestly absent.Comment: 18 pages, LaTeX, few misprints are corrected; one section is remove
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
Felix Alexandrovich Berezin and his work
This is a survey of Berezin's work focused on three topics: representation
theory, general concept of quantization, and supermathematics.Comment: LaTeX, 27 page