5,240 research outputs found
Sedeonic relativistic quantum mechanics
We represent sixteen-component values "sedeons", generating associative
noncommutative space-time algebra. We demonstrate a generalization of
relativistic quantum mechanics using sedeonic wave functions and sedeonic
space-time operators. It is shown that the sedeonic second-order equation for
the sedeonic wave function, obtained from the Einstein relation for energy and
momentum, describes particles with spin 1/2. We show that for the special types
of wave functions the sedeonic second-order equation can be reduced to the set
of sedeonic first-order equations analogous to the Dirac equation. At the same
time it is shown that these sedeonic equations differ in space-time properties
and describe several types of massive and corresponding massless particles. In
particular we proposed four different equations, which could describe four
types of neutrinos.Comment: 22 pages, 3 table
Two-logarithm matrix model with an external field
We investigate the two-logarithm matrix model with the potential
related to an exactly solvable
Kazakov-Migdal model. In the proper normalization, using Virasoro constraints,
we prove the equivalence of this model and the Kontsevich-Penner matrix model
and construct the 1/N-expansion solution of this model.Comment: 15pp., LaTeX, no figures, reference adde
Effective Action and Measure in Matrix Model of IIB Superstrings
We calculate an effective action and measure induced by the integration over
the auxiliary field in the matrix model recently proposed to describe IIB
superstrings. It is shown that the measure of integration over the auxiliary
matrix is uniquely determined by locality and reparametrization invariance of
the resulting effective action. The large-- limit of the induced measure for
string coordinates is discussed in detail. It is found to be ultralocal and,
thus, possibly is irrelevant in the continuum limit. The model of the GKM type
is considered in relation to the effective action problem.Comment: 9pp., Latex; v2: the discussion of the large N limit of the induced
measure is substantially expande
On local anesthetic action of some dimethylacetamide compounds
The study aim was to explore local anesthetic properties of some tertiary and quaternary derivatives of dimethylacetamid
Generalized matrix models and AGT correspondence at all genera
We study generalized matrix models corresponding to n-point Virasoro
conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT
correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge
theories with generalized quiver diagrams. We obtain the generalized matrix
models from the perturbative evaluation of the Liouville correlation functions
and verify the consistency of the description with respect to degenerations of
the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2
gauge theory as the spectral curve of the generalized matrix model, thus
providing a check of AGT correspondence at all genera.Comment: 19 pages; v2: version to appear in JHE
Selberg Integral and SU(N) AGT Conjecture
An intriguing coincidence between the partition function of super Yang-Mills
theory and correlation functions of 2d Toda system has been heavily studied
recently. While the partition function of gauge theory was explored by
Nekrasov, the correlation functions of Toda equation have not been completely
understood. In this paper, we study the latter in the form of Dotsenko-Fateev
integral and reduce it in the form of Selberg integral of several Jack
polynomials. We conjecture a formula for such Selberg average which satisfies
some consistency conditions and show that it reproduces the SU(N) version of
AGT conjecture.Comment: 35 pages, 5 figures; v2: minor modifications; v3: typos corrected,
references adde
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